Geodesic
Extreme Points in Spaces of Analytic Functions
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 919-928

Voir la notice de l'article provenant de la source Cambridge University Press

Our aim in this paper is to obtain some theorems concerning spaces of analytic functions on a finite open Riemann surface R which extend known results for the disc △ = {|z| < 1}. Suppose that R has a smooth boundary bR consisting of t closed curves, and that the interior genus of R is s. The first Betti number of R is then r = 2s + t — 1. 
Gamelin, T. W.; Voichick, M. Extreme Points in Spaces of Analytic Functions. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 919-928. doi: 10.4153/CJM-1968-089-5
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