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An application of capacitary functions to an inverse inclusion problem. (English) Zbl 1254.30062

Summary: An efficient application of capacitary functions for compact subsets of the Royden harmonic boundary to an inverse inclusion problem concerning spaces of Dirichlet finite and mean bounded harmonic functions in the classification theory of Riemann surfaces is given.

MSC:

30F15 Harmonic functions on Riemann surfaces
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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Full Text: Euclid