THE UNIFORMIZATION THEOREM

POINCARÉ, H.

Sur L'Uniformisation des Fonctions Analytiques.

Berlin, Stockholm, Paris, Almqvist & Wiksell, 1908. 4to. Bound in contemporary half cloth with gilt lettering to spine. In "Acta Mathematica", Vol, 31, 1908. Entire volume offered. Stamps to title page, otherwise a fine and clean copy. Pp. 1-64. [Entire volume: (8), 408, (2), 12 pp].

First appearance of Poincaré's important paper in which he presented the first solution to the problem of the uniformization of curves - now know as The Uniformization Theorem.

Clebsch and Riemann tried to solve the problem of the uniformization for curves. "In 1882 Klein gave a general uniformization theorem, but the proof was not complete. In 1883 Poincaré announced his general uniformization theorem but he too had no complete proof. Both Klein and Poincaré continued to work hard to prove this theorem but no decisive result was obtained for twent-five years. In 1907 Poincare (in the offered paper) and Paul Koebe independently gave a proof of this uniformization theorem...With the theorem on uniformization now rigorously established an improved treatment of algebraic functions and their integrals has become possible." (Morris Kline).

Order-nr.: 49616