Barrett: Failure of averaging on multiply connected domains

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David E. Barrett
Failure of averaging on multiply connected domains
Annales de l'institut Fourier, 40 no. 2 (1990), p. 357-370, doi: 10.5802/aif.1216
Article PDF | Reviews MR 92b:30050 | Zbl 0726.30034

Résumé - Abstract

We show that for every open Riemann surface $X$ with non-abelian fundamental group there is a multiple-valued function $f$ on $X$ such that the fiberwise convex hull of the graph of $f$ fails to contain the graph of a single-valued holomorphic function on $X$.

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