Search Results for Conformal

Biographies

1. Sasaki biography
   
   • These included several different geometry courses, including projective geometry, conformal geometry, non-Euclidean geometry, differential geometry, and synthetic geometry.
     
   • One of them is a series of three papers on the relations between the structure of spaces with normal conformal connections and their holonomy groups.
     
   • During the early 1940s Sasaki wrote a major text Geometry of Conformal Connection in Japanese, completing the manuscript of the book in 1943.
     
   • Weyl opened the way to the conformal differential geometry of Riemannian spaces in which one studies the properties of the spaces invariant under the so-called conformal transformation of the Riemannian metric.
     
   • He discovered a tensor, now called Weyl's conformal curvature tensor, whose vanishing is a necessary condition that the space be conformally flat, that is to say, that the space can be mapped conformally on the Euclidean space.
     
   • studied exclusively the conformal properties of a Riemannian space itself and paid only slight attention to the conformal properties of curves and surfaces immersed in a Riemannian space.
     
   • S Sasaki, Y Muto, and K Yano have developed, since 1938, the conformal theory of curves and surfaces in a conformally connected space as well as in a Riemannian space.
     
   • This book contains almost all the results mentioned above in the geometry of conformal connection.
     
   • Among the topics Sasaki contributed to over a long research career were Lie geometry of circles, conformal connections, projective connections, holonomy groups, Hermitian manifolds, geometry of tangent bundles and almost contact manifolds (now called Sasaki manifolds), global problems on curves and surfaces in various spaces.
     

2. Schramm biography
   
   • He undertook research with William Thurston as his thesis advisor, and submitted his thesis Packing Two-Dimensional Bodies With Prescribed Combinatorics And Applications To The Construction of Conformal and Quasi-Conformal Mappings in 1990.
     
   • His work in a spectacular series of papers has led to major progress in probability theory, in the theory of percolation and of random walks, as well as in related topics of conformal field theory.
     
   • For his contributions to discrete conformal geometry, where he discovered new classes of circle patterns described by integrable systems and proved the ultimate results on convergence to the corresponding conformal mappings, and for the discovery of the Stochastic Loewner Process as a candidate for scaling limits in two dimensional statistical mechanics.
     
   • In fact, Brownian motion enjoys conformal invariance, which is far richer.
     
   • Many other random systems, such as critical percolation and the critical Ising model of magnetism, also seem to exhibit conformal invariance in the scaling limit.
     
   • This conformal invariance implies that certain paths arising naturally from these processes fall into a particular one-parameter family of random fractal paths called Stochastic Loewner Evolution, or SLE.
     
   • Of particular note is the rigorous establishment of the existence and conformal invariance of critical scaling limits of a number of 2D lattice models arising in statistical physics.
     

3. Warschawski biography
   
   • Warschawski moved to Basel with his supervisor and there completed working on his thesis on the boundary behaviour of conformal mappings.
     
   • Warschawski published a major 30 page paper On the higher derivatives at the boundary in conformal mapping in the Transactions of the American Mathematical Society in 1935 but had to move from one short term post to the next until he was offered a permanent position in 1939 at Washington University in St Louis.
     
   • He continued to undertake research on conformal mapping publishing On conformal mapping of regions bounded by smooth curves in 1951.
     
   • In 1955 he published two papers in Experiments in the computation of conformal maps published in the National Bureau of Standards Applied Mathematics Series.
     
   • The first was a single author paper On the solution of the Lichtenstein-Gershgorin integral equation in conformal mapping.
     
   • Theory while the second, On the solution of the Lichtenstein-Gershgorin integral equation in conformal mapping.
     
   • With careful scholarship, he made lasting contributions to the theory of complex analysis, particularly to the theory of conformal mappings.
     

4. Kober biography
   
   • The British Admiralty approached Kober during World War II and asked him to produce a dictionary of conformal mappings which might be useful in war related research.
     
   • His Dictionary of conformal representations appeared in five separate volumes between 1944 and 1948.
     
   • it should be of considerable help to those concerned with the use of conformal maps in various branches of applied mathematics.
     
   • The conformal mappings described in the book are by and large arranged according to the analytic functions giving rise to them, the author having found that this permits a more systematic classification than an arrangement according to geometric properties of domains.
     

5. Caratheodory biography
   
   • He examined conformal representations of simply connected regions and he developed a theory of boundary correspondence.
     
   • Caratheodory wrote many fine books including Lectures on Real Functions (1918), Conformal representation (1932), Calculus of Variations and Partial Differential Equations (1935), Geometric Optics (1937), Real functions Vol.
     
   • Caratheodory's Conformal representation .
     

6. Ahlfors biography
   
   • I had the incredible luck of hitting upon a new approach, based on conformal mappings, which, with very considerable help from Nevanlinna and Polya, led to a proof of the full conjecture.
     
   • Lectures on quasi-conformal mappings (1966) and Conformal invariants (1973).
     

7. Keen biography
   
   • In the early 1960s, Bers and Ahlfors showed that the space of conformal structures on a given Riemann surface can be modelled on a Banach space with a real analytic structure.
     
   • Keen defined the set of parameters for this space in terms of the hyperbolic structure of a given surface determined by the conformal structure.
     
   • By this time, Bers had proved that the space of conformal structures on Riemann surfaces admits a complex analytic structure, and Maskit had defined an embedding of that space into complex n-dimensional space for appropriate n.
     

8. Christoffel biography
   
   • Christoffel published papers on function theory including conformal mappings, geometry and tensor analysis, Riemann's o-function, the theory of invariants, orthogonal polynomials and continued fractions, differential equations and potential theory, light, and shock waves.
     
   • Some of Christoffel's early work was on conformal mappings of a simply connected region bounded by polygons onto a circle.
     
   • This work on conformal mappings was published in four papers between 1868 and 1870.
     

9. Chang biography
   
   • The Ruth Lyttle Satter Prize is awarded to Sun-Yung Alice Chang for her deep contributions to the study of partial differential equations on Riemannian manifolds and in particular for her work on extremal problems in spectral geometry and the compactness of isospectral metrics within a fixed conformal class on a compact 3-manifold.
     
   • We have also applied this approach in conformal geometry to the isospectral compactness problem on 3-manifolds when the metrics are restricted in any given conformal class.
     

10. Julia biography
    
    • Volume 3 contains four parts: (i) Functional equations and conformal mapping; (ii) Conformal mapping; (iii) General lectures; and (iv) Isolated works in analysis on Implicit function defined by the vanishing of an active function, and on certain series.
      
    • As the author himself points out in the preface to the first volume, the most important of these principles is the conformal correspondence between two regions of planar character or two Riemann surfaces realized by an analytic function.
      

11. Rado biography
    
    • His first paper On the roots of algebraic equations was published in 1921 and in the following year he published his first paper on conformal mappings.
      
    • Their approaches were very different, Rado's being via conformal mappings.
      
    • He used conformal mappings of polyhedra, applying a limit theorem to certain approximations to obtain the minimal surface required.
      

12. Beurling biography
    
    • Beurling's leading idea was to find new estimates for the harmonic measure by introducing concepts, and problems, which are inherently invariant under conformal mapping.
      
    • Among his papers let us mention Exceptional sets (1935), Sur les integrales de Fourier absolument convergentes et leur application a une transformation fonctionelle (1938), Sur les spectres des fonctions (1949), (with Ahlfors) On the boundary correspondance under quasi-conformal map (1956), and (with Paul Malliavin) On the closure of characters and the zeros of entire functions (1967).
      

13. Schottky biography
    
    • His doctoral thesis is an important contribution to conformal mappings of multiply connected plane domains.
      
    • Schottky's thesis also discusses conformal mappings of domains bounded by circular and conic arcs.
      

14. Rey Pastor biography
    
    • His lectures there on n-dimensional geometry and conformal mappings, developing the work of Schwarz, was written up by Esteban Terrades who attended the lectures, and the course was published in Catalan.
      
    • His second course, given in 1921, was a specialised one for engineering students and included the following topics: functions of a complex variable, conformal mapping, advanced geometry (non-euclidean), mathematical analysis and mathematical methodology.
      

15. Robertson biography
    
    • Robertson was awarded his doctorate from the California Institute of Technology in 1925 after submitting his dissertation On the Dynamical Space-Time which Contains a Conformal Euclidean 3-Space.
      
    • His contributions to differential geometry came in papers such as: The absolute differential calculus of a non-Pythagorean non-Riemannian space (1924); Transformation of Einstein space (1925); Dynamical space-times which contain a conformal Euclidean 3-space (1927); Note on projective coordinates (1928); (with H Weyl) On a problem in the theory of groups arising in the foundations of differential geometry (1929); Hypertensors (1930); and Groups of motion in space admitting absolute parallelism (1932).
      

16. Zhukovsky biography
    
    • In mathematics today the conformal mapping of the complex plane z → z + 1/z is called the Joukowski transformation.
      
    • a means of designing aerofoils using conformal mappings and the techniques of complex variables.
      

17. Titeica biography
    
    • Among these many topics were surfaces of constant curvature, ruled surfaces, metrical properties of space, minimal surfaces, Weingarten congruencies, conformal representation, and conformal geometry.
      

18. Possel biography
    
    • In 1931 he published a result on the conformal mapping of a simply connected domain in a Gottingen journal.
      
    • In 1939 he published Sur la representation conforme d'un domaine a connexion infinie sur un domaine a fentes paralleles in which he developed further the ideas on conformal mapping of a simply connected domain which he had published in 1931.
      

19. Henrici Peter biography
    
    • The first volume Power series - integration - conformal mapping - location of zeros first appeared in 1974, the second volume Special functions - integral transforms - asymptotics - continued fractions first appeared in 1977, and the third and final volume Discrete Fourier analysis - Cauchy integrals - construction of conformal maps - univalent functions first appeared in 1986.
      

20. Schwarz biography
    
    • One important area which Schwarz worked on was that of conformal mappings.
      
    • It was in this work that he defined a conformal mapping of a triangle with arcs of circles as sides onto the unit disc which is now known as the 'Schwarz function'.
      

21. Zarankiewicz biography
    
    • However, he taught a course on conformal mappings, one of his current research interests, for a semester at Tomsk in 1936.
      
    • played an important role in the development of the theory of the kernel and its generalisations to several variables, notably to pseudo-conformal transformations in space of more than three dimensions.
      

22. Calugareanu biography
    
    • During the same period of rapid development of aerodynamics, studies connected with the theory of conformal representation became of great interest.
      
    • Calugareanu investigated necessary and sufficient conditions for univalence of functions holomorphic in a disc and obtained results in the theory of conformal representation of multiply connected domains.
      

23. Lavrentev biography
    
    • Lavrentev is remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.
      
    • In the 1940s he developed the theory of quasi-conformal mappings which gave a new geometrical approach to partial differential equations.
      

24. Peschl biography
    
    • He obtained his doctorate in 1931 for the thesis Uber die Krummung von Niveaukurven bei der konformen Abbildung einfachzusammenhangender Gebiete auf das Innere eines Kreises; eine Verallgemeinerung eines Satzes von E Study (On the curvature of curves on the plane in the case of conformal mapping of simply connected domains onto the interior of a circle.
      
    • The titles of the chapters are: Algebra and geometry of complex numbers; Fundamental topological concepts, sets, sequences of complex numbers and infinite series; Functions, real and complex differentiability and holomorphy; Integral theorems and their consequences; Winding number and curves homologous to zero; Taylor development of holomorphic functions; Elementary transcendental functions; Laurent series, isolated singularities and residue calculus; Holomorphic and meromorphic functions obtained by limiting processes; Analytic continuation; and Conformal mappings.
      

25. Gronwall biography
    
    • Gronwall's work contains classical analysis (Fourier series, Gibbs phenomenon, summability theory, Laplace and Legendre series), differential and integral equations, analytic number theory (transcendental numbers, divisor function, L-function of Dirichlet), complex function theory (Dirichlet L-series, conformal mappings, univalent functions), differential geometry, mathematical physics (problems of elasticity, ballistics, induction, potential theory, kinetic theory of gases, optics), nomography, atomic physics (wave mechanics of hydrogen and helium atom, lattice theory of crystals) and physical chemistry where he is especially known as a very important contributor.
      

26. Harriot biography
    
    • He exhibited the logarithmic spiral as the stereographic projection of a loxodrome on a sphere, a projection he proved to be conformal.
      

27. Yano biography
    
    • To gauge the magnitude of his contribution to differential geometry, it suffices to recall his mathematical work, extending over the past four decades, which covers such diverse areas of geometry as affine, projective and conformal connections, geometry of Hermitian and Kahlerian manifolds, holonomy groups, automorphism groups of geometric structures, harmonic integrals, tangent and cotangent bundles, submanifolds, and integral formulas in Riemannian geometry.
      

28. Beltrami biography
    
    • He translated Gauss's work on conformal representation into Italian.
      

29. Bergman biography
    
    • Its results were applied, on the one hand, to fluid dynamics, conformal mapping and potential theory and led, on the other hand, to the "Bergman kernel function" which is one of his major achievements in pure mathematics.
      
    • He lectured first at the Massachusetts Institute of Technology in Cambridge, Massachusetts, where he gave a series of lectures on Theory of pseudo-conformal transformations and its connection with differential geometry during 1939-40.
      
    • He is also known for applications of the kernel function to conformal mappings which he explains in his classic text The Kernel Function and Conformal Mapping (1950).
      

30. Teichmuller biography
    
    • He introduced quasi-conformal mappings and differential geometric methods into complex analysis.
      

31. Kochina biography
    
    • After considering the problem of conformal mapping on the half-plane of finite polygonal regions bounded by straight lines and circular arcs she applied these ideas to the physical problem of the two-dimensional seepage flow of ground water in an earth dam of a particular shape.
      

32. Milne Archibald biography
    
    • He read papers at meetings of the Society such as Notes on the equation of the parabolic cylinder on Friday 9 January 1914, The Conformal Representation of the Quotient of two Bessel Functions on 24 January 1916, and Note on the Peano-Baker method of solving linear differential equations on 11 February 1916.
      

33. Todd John biography
    
    • He studied methods for evaluating mathematical functions, generating random numbers (for Monte Carlo calculations), conformal mappings, and computations with matrices.
      

34. Feigl biography
    
    • His doctoral dissertation was on conformal mappings.
      

35. Hille biography
    
    • Then Hille began working with Marcel Riesz on conformal mappings and submitted a thesis on that topic in 1916; for this he was awarded a Lic.
      

36. Cartwright biography
    
    • To prove the theorem she used a new approach, applying a technique introduced by Ahlfors for conformal mappings.
      

37. Fejer biography
    
    • Fejer collaborated to produce important papers, one with Caratheodory on entire functions in 1907 and another major work with Riesz in 1922 on conformal mappings.
      

38. Spencer biography
    
    • Spencer's work in the late 1940s and early 1950 was on the theory of the conformal mapping of plane regions in which domain functions, variational methods, and the problem of coefficient domains are central considerations.
      

39. Hsiung biography
    
    • Topics he then investigated include two-dimensional Riemannian manifolds with boundary (uniqueness and isoperimetic inequalities), groups of conformal transformations of a compact Riemannian manifold, curvature and characteristic classes, complex structure, and isospectral almost-L-manifolds.
      

40. Liouville biography
    
    • Liouville contributed to differential geometry studying conformal transformations.
      

41. Stoilow biography
    
    • After a fairly standard introduction to the general theory, beginning with power series, he goes on, in volume 1, to look at topics such as entire and meromorphic functions, doubly periodic functions, conformal mapping on the boundary of a Jordan region, multiple-valued functions, and applications of modular functions to the Picard circle of ideas.
      

42. Milne-Thomson biography
    
    • Formulae special to particular branches of knowledge are not included, with the exception of some conformal transformations which cover ground common to several sciences.
      

43. Vranceanu biography
    
    • Other topics he studied include the absolute differential calculus of congruences, analytical mechanics, partial differential equations of the second order, non-holonomic unitary theory, conformal connection spaces, metrics in spherical and projective spaces, Lie groups, global differential geometry, discrete groups of affine connection spaces, locally Euclidean connection spaces, Riemannian spaces of constant connection, differentiable varieties, embedding of lens spaces into Euclidean space, tangent vectors of spheres and exotic spheres, the equivalence method, non-linear connection spaces, and the geometry of mechanical systems.
      

44. Luzin biography
    
    • In the theory of boundary properties of analytic functions he proved an important result in 1919 on the invariance of sets of boundary points under conformal mappings.
      

45. Denjoy biography
    
    • It studies the asymptotic behaviour of integral functions of finite order, Weierstrass products of integral functions and the boundary behaviour of conformal representations.
      

46. Schouten biography
    
    • Influenced by Weyl and Eddington, Schouten investigated affine, projective and conformal mappings.
      

47. Knopp biography
    
    • Chapter IV: Analytic functions and conformal mapping.
      

48. Dinghas biography
    
    • The final part containing chapters on the maximum principle and the distribution of values, geometric function theory and conformal mapping, and Nevanlinna theory.
      

49. Courant biography
    
    • His thesis was entitled Uber die Anwendung des Dirichletschen Prinzipes auf die Probleme der konformen Abbildung (On the application of Dirichlet's principle to the problems of conformal mappings).
      

50. Radon biography
    
    • During 1918-19 he worked on affine differential geometry, then in 1926 he considered conformal differential geometry.
      

51. Vallee Poussin biography
    
    • After 1925 Vallee Poussin turned to complex variable, potential theory and conformal representation.
      

52. Polya biography
    
    • He also worked on conformal mappings and potential theory, and he was led to study boundary value problems for partial differential equations and the theory of various functionals connected with them.
      

53. Wolf Frantisek biography
    
    • By means of conformal representation, simply connected domains with rectifiable boundaries are reduced to the circle.
      

54. Ostrowski biography
    
    • These are determinants, linear algebra, algebraic equations, multivariate algebra, formal algebra, number theory, geometry, topology, convergence, theory of real functions, differential equations, differential transformations, theory of complex functions, conformal mappings, numerical analysis and miscellany.
      

55. Privalov biography
    
    • He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere.
      

56. Klein biography
    
    • He wrote Riemanns Theorie der algebraischen Funktionen und ihre Integrals in 1882 which treats function theory in a geometric way connecting potential theory and conformal mappings.
      

57. Douglas biography
    
    • His publications from this period are Normal congruences and quadruply infinite systems of curves in space (1924), and A criterion for the conformal equivalence of a Riemann space to a Euclidean space (1925).
      

58. Suvorov biography
    
    • Another area on which Suvorov worked was the theory of conformal mappings and quasi-formal mappings.
      
    • This important result served as a source for the investigations of principally new character: The above-mentioned theorem cannot be explained even in the case of conformal mappings in the framework of the usual theory of boundary correspondence by prime ends since the limit sets with respect to two sequences of points that converge to the same prime end may be different.
      
    • In connection with this, G D Suvorov posed the problem whether there exist conformal invariant compactifications of a simply connected plane domain (in the first instance, metrizable) different from the Caratheodory (and from the "trivial" one from the point of view of the known theory of the one-point and the Stone-Cech compactifications), and about the description of all such compactifications.
      
    • As it turns out, infinitely many such conformal-invariant compactifications, metrizable as well as nonmetrizable, exist.
      
    • Thus the new formulation of the problem is interesting and useful; each new conformal-invariant compactification furnishes new boundary properties of conformal mappings.
      
    • G D Suvorov and his students have constructed and studied two entirely new complete lattices of conformal-invariant compactifications.
      
    • He also succeeded in obtaining a description of all conformal-invariant compactifications of a simply connected plane domain; moreover, it turns out that the family of all such compactifications constitutes a complete lattice.
      
    • Caratheodory (1913) introduced for the first time a compactification of a simply connected domain by means of boundary elements, which he called "prime ends", and proved that they are conformal invariants.
      

59. Fatou biography
    
    • Although not giving a complete solution, Fatou's work also made a major contribution to finding a solution to the related question of whether conformal mapping of Jordan regions onto the open disc can be extended continuously to the boundary.
      

60. Zygmund biography
    
    • Conformal mapping is discussed relatively late.
      

61. Schlafli biography
    
    • Other papers which he published investigate a variety of topics such as partial differential equations, the motion of a pendulum, the general quintic equation, elliptic modular functions, orthogonal systems of surfaces, Riemannian geometry, the general cubic surface, multiply periodic functions, and the conformal mapping of a polygon on a half-plane.
      

62. Riemann biography
    
    • However, Riemann's thesis is a strikingly original piece of work which examined geometric properties of analytic functions, conformal mappings and the connectivity of surfaces.
      

63. Lindelof biography
    
    • He also wrote on conformal mappings.
      

64. Walsh Joseph biography
    
    • He studied the relative location of the zeros of pairs of rational functions, zeros and topology of extremal polynomials, the critical points and level lines of Green's functions and other harmonic functions, conformal mappings, Pade approximation, and the interpolation and approximation of continuous, analytic or harmonic functions.
      

65. Peirce Charles biography
    
    • On the mathematical side, coming out of his work for the Coast Survey, we mention that he was interested in conformal map projections where he invented a quincuncial map projection using elliptic functions.
      

History Topics

Famous Curves

Societies etc

1. AMS Bôcher Prize
   
   • for his work on the application of partial differential equations to differential geometry, in particular his completion of the solution to the Yamabe Problem in "Conformal deformation of a Riemannian metric to constant scalar curvature".
     

2. BMC 1983
   
   • Sullivan, D P Conformal dynamical systems: a survey of classical and recent results .
     

3. BMC 1972
   
   • Ferrand, M O J L Quasi-conformal mappings of manifolds and generalisations .
     

4. BMC 2000
   
   • Tillmann, U Moduli spaces of Riemann surfaces and conformal field theory .
     

5. BMC 2008
   

6. International Congress Speakers
   
   • Menahem Max Schiffer, Extremum Problems and Variational Methods in Conformal Mapping.
     
   • Boris L Feigin, Conformal Field Theory and Cohomologies of the Lie Algebra of Holomorphic Vector Fields on a Complex Curve.
     
   • Alexandre Varchenko, Multidimensional Hypergeometric Functions in Conformal Field Theory, Algebraic K-Theory, Algebraic Geometry.
     
   • Sun-Yung Alice Chang and Paul Chien-Ping Yang, Non-linear Partial Differential Equations in Conformal Geometry.
     

7. European Mathematical Society Prizes
   
   • whose most striking result is the proof of existence and conformal invariance of the scaling limit of crossing probabilities for critical percolation on the triangular lattice.
     

8. AMS Steele Prize
   
   • for his expository work in "Complex analysis", and in "Lectures on quasiconformal mappings", and "Conformal invariants".
     

9. AMS Satter Prize
   
   • for her deep contributions to the study of partial differential equations on Riemannian manifolds and in particular for her work on extremal problems in spectral geometry and the compactness of isospectral metrics within a fixed conformal class on a compact 3-manifold.
     

10. BMC 1973
    
    • Eke, B GBehaviour of a conformal map at a boundary point .
      

References

1. References for Weyl
   
   • R Penrose, Hermann Weyl, space-time and conformal geometry, Hermann Weyl, 1885-1985 (Eidgenossische Tech.
     

2. References for Caratheodory
   
   • A Shields, Caratheodory and conformal mapping, The Mathematical Intelligencer 10 (1) (1988), 18-22.
     

Additional material

1. Carathéodory: 'Conformal representation
   
   • Caratheodory: Conformal representation .
     
   • In 1931 Caratheodory's book entitled Conformal representation was published by Cambridge University Press.
     
   • If the sense of rotation of a tangent is preserved, an isogonal transformation is called conformal.
     
   • A quite different conformal representation of the sphere on a plane area is given by Mercator's Projection; in this the spherical earth, cut along a meridian circle, is conformally represented on a plane strip.
     
   • A comparison of two maps of the same country, one constructed by stereographic projection of the spherical earth and the other by Mercator's Projection, will show that conformal transformation does not imply similarity of corresponding figures.
     
   • Other non-trivial conformal representations of a plane area on a second plane area are obtained by comparing the various stereographic projections of the spherical earth which correspond to different positions of the centre of projection on the earth's surface.
     
   • It was considerations such as these which led Lagrange (1736-1813) in 1779 to obtain all conformal representations of a portion of the earth's surface on a plane area wherein all circles of latitude and of longitude are represented by circular arcs.
     
   • In 1822 Gauss (1777-1855) stated and completely solved the general problem of finding all conformal transformations which transform a sufficiently small neighbourhood of a point on an arbitrary analytic surface into a plane area.
     
   • This was first pointed out by Riemann (1826-1866), whose Dissertation (1851) marks a turning-point in the history of the problem which has been decisive for its whole later development; Riemann not only introduced all the ideas which have been at the basis of all subsequent investigation of the problem of conformal representation, but also showed that the problem itself is of fundamental importance for the theory of functions.
     
   • http://www-history.mcs.st-andrews.ac.uk/Extras/Caratheodory_conformal.html .
     

2. Donald C Spencer's publications
   
   • D C Spencer, Distortion in Conformal Mapping (Brown University, 1941).
     
   • S Bergman and D C Spencer, On distortion in pseudo-conformal mapping, Trans.
     
   • S Bergman and D C Spencer, A property of pseudo-conformal transformations in the neighborhood of boundary points, Duke Math.
     
   • A C Schaeffer and D C Spencer, A general class of problems in conformal mapping, Proc.
     
   • D C Spencer, Some problems in conformal mapping, Bull.
     
   • A C Schaeffer and D C Spencer, A variational method in conformal mapping, Duke Math.
     
   • M Schiffer and D C Spencer, On the conformal mapping of one Riemann surface into another, Ann.
     
   • A C Schaeffer and D C Spencer, A variational method for simply-connected domains, Construction and applications of conformal maps, Proc.
     
   • Construction and applications of conformal maps, Proc.
     

3. Oswald Veblen Publications
   
   • (b) "Conformal Tensors and Connections", Proc.
     
   • 1935 (a) "Formalism for Conformal Geometry", Proc.
     
   • (b) "A Conformal Wave Equation", Proc.
     

4. Konrad Knopp: Texts
   
   • Volume I contains more than 300 elementary problems dealing with fundamental concepts, infinite sequences and series, functions of a complex variable, conformal mapping, and more.
     
   • Conformal Mapping .
     

5. L R Ford - Automorphic Functions
   
   • Chapter VIII gives a thorough treatment of conformal mapping, including the mapping of a plane simply connected region on a circle (with particular attention to the behaviour of the mapping function on the boundary), the mapping of limit regions, and of simply connected finite-sheeted regions.
     

6. Einar Hille: 'Analytic Function Theory
   
   • The main theory begins in Chapter 4 with the definition of holomorphic functions, the Cauchy-Riemann equations, inverse functions, and the elements of conformal mapping.
     

7. EMS obituary
   
   • Conformal mapping of one complex variable upon another was to him a fruitful way of relating significantly the shapes of apparently distinct forms of shell fish.
     

8. W H Young addresses ICM 1928 Part 2
   
   • We have, for instance, been told by the enquirer himself, of the frigid reception accorded to his question: What is the physical analogue of the most general group of conformal transformations of four-dimensional space that leaves unaltered the equations of Maxwell-Lorentz? .
     

Quotations

Chronology

1. Chronology for 1920 to 1930
   
   • Fejer and Riesz publish an important work on conformal mappings.
     

2. Mathematical Chronology
   
   • Fejer and Riesz publish an important work on conformal mappings.