Dirichlet solutions on bordered Riemann surfaces and quasiconformal mappings
type: Item
instance of: scholarly article
title: Dirichlet solutions on bordered Riemann surfaces and quasiconformal mappings
zbMATH Open document ID: 1065.30014
DOI: 10.1007/BF02787759
author: Hiroshige Shiga
published in: Journal d'Analyse Mathématique
publication date: 2004-11-01T00:00:00Z
review text: Given a compact bordered Riemann surface \(S\) and a continuous function \(f\) on \(\partial S\), let \(H^S_f\) denote the harmonic function on \(S\) with the boundary value \(f\). It is shown that if \(\varphi_n:S_0\to S_n\) is a sequence of quasiconformal mappings such that the maximal dilatations \(K(\varphi_n)\to 1\), then \(H^{S_n}_{f\circ \varphi^{-1}_n}\circ\varphi_n\Rightarrow H^{S_0}_f\). Another result is real analyticity of \(t\mapsto H^{S_t}_{f\circ\varphi^{-1}_t}\circ\varphi_t\) for quasiconformal homeomorphisms \(\varphi_t\) defined by Beltrami differentials \(\mu_t(z)\).
Mathematics Subject Classification ID: 30C62
zbMATH DE Number: 2112863
zbMATH Keywords: quasiconformal mapping
zbMATH Keywords: Teichmüller space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02787759
OpenAlex ID: W2088727618
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description: scientific article; zbMATH DE number 2112863