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arXiv · 1102.4987

On $\mu$-conformal homeomorphisms and boundary correspondence

Vladimir Gutlyanskii·Ken-ichi Sakan·Toshiyuki Sugawa
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Abstract

We study the boundary correspondence under $\mu$-homeomorphisms $f$ of the open upper half-plane onto itself. Sufficient conditions are given for $f$ to admit a homeomorphic extension to the closed half-plane with prescribed boundary regularity. The proofs are based on the modulus estimates for semiannuli in terms of directional dilatations of $f$ which might be of independent interest.

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Vladimir Gutlyanskii, Ken-ichi Sakan, Toshiyuki Sugawa. 2011-02-24. On $\mu$-conformal homeomorphisms and boundary correspondence. https://arxiv.org/abs/1102.4987

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