Some Theorems on Open Riemann Surfaces
- 1 October 1951
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 3, 141-145
- https://doi.org/10.1017/s0027763000012277
Abstract
Let F be an open Riemann surface spread over the z-plane. We say that F is of positive or null boundary, according as there exists a Green’s function on F or not, Let u(z) be a harmonic function on Fand be its Dirichlet integral As R. Nevanlinna proved, if F is of null boundary, there exists no one-valued non-constant harmonic function on F5 whose Dirichlet integral is finite, This Nevanlinna’s theorem was proved very simply by Kuroda.Keywords
This publication has 1 reference indexed in Scilit:
- The Conformal Mapping of Simply-Connected Riemann SurfacesAnnals of Mathematics, 1949