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arXiv · 1805.04313

Quasiconformal and HQC mappings between Lyapunov Jordan domains

Vladimir Bozin Miodrag Mateljević
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Abstract

Let $h$ be a quasiconformal (qc) mapping of the unit disk $\mathbb{U}$ onto a Lyapunov domain. We show that $h$ maps subdomains of Lyapunov type of $\mathbb{U}$, which touch the boundary of $\mathbb{U}$, onto domains of similar type. In particular if $h$ is a harmonic qc (hqc) mapping of $\mathbb{U}$ onto a Lyapunov domain, using it, we prove that $h$ is co-Lipschitz (co-Lip) on $\mathbb{U}$. This settles an open intriguing problem.

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Vladimir Bozin Miodrag Mateljević. 2018-05-11. Quasiconformal and HQC mappings between Lyapunov Jordan domains. https://arxiv.org/abs/1805.04313

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