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Bi-Lipschitz property and distortion theorems for planar harmonic mappings with $M$-linearly connected holomorphic part

Jie Huang|Jian-Feng Zhu
대한수학회 (The Korean Mathematical Society)|2018.09|대한수학회보 (Bulletin of the KMS)|제55권 제5호|pp. 1419-1431

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참고문헌

키워드

quasiconformal mappingharmonic mappingbi-Lipschitz mapping$M$-linearly connected domain
주제분류수학

초록

Let $f=h+\overline{g}$ be a harmonic mapping of the unit disk $\mathbb D$ with the holomorphic part $h$ satisfying that $h$ is injective and $h(\mathbb D)$ is an $M$-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for $f$ to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

Abstract

Let $f=h+\overline{g}$ be a harmonic mapping of the unit disk $\mathbb D$ with the holomorphic part $h$ satisfying that $h$ is injective and $h(\mathbb D)$ is an $M$-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for $f$ to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

참고문헌 (14)

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