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


Published:20150206
Printed: Jun 2015
Xiaomin Tang,
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P.R. China
Taishun Liu,
Department of Mathematics, Huzhou University, Huzhou, Zhejiang 313000, P.R. China
Abstract
Let $B_{p_1, p_2}=\{z\in\mathbb{C}^n:
z_1^{p_1}+z_2^{p_2}+\cdots+z_n^{p_2}\lt 1\}$
be an egg domain in $\mathbb{C}^n$. In this paper, we first
characterize the Kobayashi metric on $B_{p_1, p_2}\,(p_1\geq
1, p_2\geq 1)$,
and then establish a new type of the classical boundary Schwarz
lemma at $z_0\in\partial{B_{p_1, p_2}}$ for holomorphic selfmappings
of $B_{p_1, p_2}(p_1\geq 1, p_2\gt 1)$, where $z_0=(e^{i\theta},
0, \dots, 0)'$ and $\theta\in \mathbb{R}$.
MSC Classifications: 
32H02, 30C80, 32A30 show english descriptions
Holomorphic mappings, (holomorphic) embeddings and related questions Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
32H02  Holomorphic mappings, (holomorphic) embeddings and related questions 30C80  Maximum principle; Schwarz's lemma, Lindelof principle, analogues and generalizations; subordination 32A30  Other generalizations of function theory of one complex variable (should also be assigned at least one classification number from Section 30) {For functions of several hypercomplex variables, see 30G35}
