Boundary Schwarz lemma for holomorphic self-mappings of strongly pseudoconvex domains

Xieping Wang; Guangbin Ren

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arXiv · 1506.01569

Boundary Schwarz lemma for holomorphic self-mappings of strongly pseudoconvex domains

Xieping Wang·Guangbin Ren

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Abstract

In this paper, we generalize a recent work of Liu et al. from the open unit ball $\mathbb B^n$ to more general bounded strongly pseudoconvex domains with $C^2$ boundary. It turns out that part of the main result in this paper is in some certain sense just a part of results in a work of Bracci and Zaitsev. However, the proofs are significantly different: the argument in this paper involves a simple growth estimate for the Carath\'eodory metric near the boundary of $C^2$ domains and the well-known Graham's estimate on the boundary behavior of the Carath\'eodory metric on strongly pseudoconvex domains, while Bracci and Zaitsev use other arguments.

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Xieping Wang, Guangbin Ren. 2015-06-04. Boundary Schwarz lemma for holomorphic self-mappings of strongly pseudoconvex domains. https://arxiv.org/abs/1506.01569

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