Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in 1907–1909. He did his thesis at Berlin, where he worked under Hermann Schwarz. He was an extraordinary professor at Leipzig from 1910 to 1914, then an ordinary professor at the University of Jena before returning to Leipzig in 1926 as an ordinary professor. He died in Leipzig.[1]
He conjectured the Koebe quarter theorem on the radii of disks in the images of injective functions, in 1907. His conjecture became a theorem when it was proven by Ludwig Bieberbach in 1916, and the function providing a tight example for this theorem became known as the Koebe function.[2]
^O'Connor, John J.; Robertson, Edmund F., "Paul Koebe", MacTutor History of Mathematics Archive, University of St Andrews
^Duren, Peter L. (1983), Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, pp. 30–31, ISBN 0-387-90795-5, MR 0708494
PaulKoebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important...
In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following: Koebe Quarter Theorem. The image of an injective analytic function...
uniformization theorem were given by Poincaré (1907) and PaulKoebe (1907a, 1907b, 1907c). PaulKoebe later gave several more proofs and generalizations. The...
at the University of Berlin, where his students included Lipót Fejér, PaulKoebe and Ernst Zermelo. In total, he advised at least 22 Ph. D students. In...
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose...
Artin in 1924 (for the system now called Artin billiard), Pekka Myrberg, PaulKoebe, Jakob Nielsen, G. A. Hedlund. The first formal treatment was developed...
pair of circles that kiss. The circle packing theorem, first proved by PaulKoebe in 1936, states that a graph is planar if and only if it is a coin graph...
Carathéodory's proof used Riemann surfaces and it was simplified by PaulKoebe two years later in a way that did not require them. Another proof, due...
D. Leipzig 1932), and Hans Richter (Ph.D. Leipzig 1936, co-advised by PaulKoebe). Van der Waerden notation Van der Waerden number Van der Waerden's conjecture...
Hollwitz (born 1989), footballer Bernhard Kadenbach (born 1933), biochemist PaulKoebe (1882–1945), mathematician Niklas Kohrt (born 1980), actor Hans Krueger...
listed below. PaulKoebe conjectures the result of the Koebe quarter theorem. The Ehrenfest model of diffusion is proposed by Tatiana and Paul Ehrenfest to...
pattern of adjacencies forms a planar graph; it was originally proved by PaulKoebe in the 1930s, and popularized by William Thurston, who rediscovered it...
Mathematics Academic advisors Karl Weierstrass Hermann von Helmholtz Notable students Heinrich Jung PaulKoebe Konrad Knopp Walter Schnee Leon Lichtenstein...
Giacomelli Corrado Gini Paul Gordan George Greenhill August Gutzmer Jacques Hadamard Gerhard Hessenberg Gregorius Itelson PaulKoebe G. V. Kolosoff Arthur...
University of Jena in 1909. In 1918, he obtained his doctorate under PaulKoebe. From 1928 he was editor of the Jahrbuch über die Fortschritte der Mathematik...
triangulated manifolds and simplicial polytopes. 1907 Henri Poincaré, PaulKoebe The uniformization theorem for simply connected Riemann surfaces. 1907...
surface is planar. The class of planar Riemann surfaces was studied by Koebe who proved in 1910, as a generalization of the uniformization theorem, that...
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