Pure and Applied Mathematics Quarterly

Volume 11 (2015)

Number 1

A new boundary rigidity theorem for holomorphic self-mappings of the unit ball in $\mathbb{C}^n$

Pages: 115 – 130

DOI: https://dx.doi.org/10.4310/PAMQ.2015.v11.n1.a5

Authors

Taishun Liu (Department of Mathematics, Huzhou University, Huzhou, China)

Xiaomin Tang (Department of Mathematics, Huzhou University, Huzhou, China)

Abstract

In this paper, we give some new boundary rigidity properties for holomorphic self-mappings of the unit ball in $\mathbb{C}^n$. Compared with the previous related work, our result only requires conditions on the first-order derivatives, thought at $n$ linearly independent different boundary points.

Keywords

holomorphic mapping, Schwarz lemma, boundary rigidity, unit ball

2010 Mathematics Subject Classification

Primary 32H02. Secondary 30C80, 32A30.

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Published 1 September 2015