Abstract
In this paper, we consider quasiconformal homeomorphisms ϕn ;S 0→S n (n = 1, 2, ...) of a bordered Riemann surfaceS 0 and discuss how the Dirichlet solutions $$H_{fo\varphi n^{ - 1} }^{S_n } $$ for a continuous functionf on ϖS 0 vary when the maximal dilatations of ϕn converge to one. Furthermore, we consider the smoothness of Dirichlet solutions for parameters of the quasiconformal deformation.
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