The Schwarz Lemma at the Boundary of the Egg Domain $B_{p_1, p_2}$ in $mathbb{C}^n$

Canadian mathematical bulletin

Taishun Liu¹  Xiaomin Tang¹ 

[1] Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P.R. China

关键词: holomorphic mapping;    Schwarz lemma;    Kobayashi metric;    egg domain;   

DOI  :  10.4153/CMB-2014-067-7

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $B_{p_1, p_2}={zinmathbb{C}^n:|z_1|^{p_1}+|z_2|^{p_2}+cdots+|z_n|^{p_2}lt 1}$ be an egg domain in $mathbb{C}^n$. In this paper, we first characterize the Kobayashi metric on $B_{p_1, p_2},(p_1geq1, p_2geq 1)$, and then establish a new type of the classical boundary Schwarz lemma at $z_0inpartial{B_{p_1, p_2}}$ for holomorphic self-mappings of $B_{p_1, p_2}(p_1geq 1, p_2gt 1)$, where $z_0=(e^{iheta},0, dots, 0)'$ and $hetain mathbb{R}$.

【 授权许可】

Unknown