Simultaneous uniformization

1960/01/01 by Lipman Bers · 8 citations
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Nonlinear Waves and Solitons #Algebraic and Geometric Analysis #Uniformization (probability theory) #Mathematics #Statistics

paper · pdf · doi:10.1090/s0002-9904-1960-10413-2

openalex publication_date 1960/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

We shall show that any two Riemann surfaces satisfying a certain condition, for instance, any two closed surfaces of the same genus g>l, can be uniformized by one group of fractional linear transformations (Theorem 1). This leads, in conjunction with previous results [2; 3], to the simultaneous uniformization of all algebraic curves of a given genus (Theorems 2-4). Theorem 5 contains an application to infinitely dimensional Teichmtiller spaces.

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