Nous démontrons que pour toute surface de Riemann ouverte , de groupe fondamental non-abélien, il existe une fonction analytique multiforme sur telle que l’enveloppe convexe par fibre du graphe de ne contienne le graphe d’aucune fonction holomorphe uniforme sur .
We show that for every open Riemann surface with non-abelian fundamental group there is a multiple-valued function on such that the fiberwise convex hull of the graph of fails to contain the graph of a single-valued holomorphic function on .
@article{AIF_1990__40_2_357_0,
author = {Barrett, David E.},
title = {Failure of averaging on multiply connected domains},
journal = {Annales de l'Institut Fourier},
volume = {40},
year = {1990},
pages = {357-370},
doi = {10.5802/aif.1216},
mrnumber = {92b:30050},
zbl = {0726.30034},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1990__40_2_357_0}
}
Barrett, David E. Failure of averaging on multiply connected domains. Annales de l'Institut Fourier, Tome 40 (1990) pp. 357-370. doi : 10.5802/aif.1216. http://gdmltest.u-ga.fr/item/AIF_1990__40_2_357_0/
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