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arXiv · 2007.12840

Boundary Schwarz lemma for harmonic mappings having zero of order $p$

Xiao-Jin Bai·Jie Huang·Jian-Feng Zhu
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Abstract

Suppose $w$ is a sense-preserving harmonic mapping of the unit disk $\mathbb{D}$ such that $w(\mathbb{D})\subseteq\mathbb{D}$ and $w$ has a zero of order $p\geq1$ at $z=0$. In this paper, we first improve the Schwarz lemma for $w$, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of $\mathbb{D}$, we further generalize this result.

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Xiao-Jin Bai, Jie Huang, Jian-Feng Zhu. 2020-07-25. Boundary Schwarz lemma for harmonic mappings having zero of order $p$. https://doi.org/10.1007/s40840-020-00980-1

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