THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS

doi:10.1007/s10473-019-0401-5

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (4): 915-926.doi: 10.1007/s10473-019-0401-5

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THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS

何乐, 涂振汉

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2017-05-29 出版日期:2019-08-25 发布日期:2019-09-12
通讯作者: Zhenhan TU E-mail:zhhtu.math@whu.edu.cn
作者简介:Le HE,E-mail:hele2014@whu.edu.cn
基金资助:
The project supported in part by the National Natural Science Foundation of China (11671306).

THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS

Le HE, Zhenhan TU

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2017-05-29 Online:2019-08-25 Published:2019-09-12
Supported by:
The project supported in part by the National Natural Science Foundation of China (11671306).

摘要/Abstract

摘要： Let B_2,p:={z∈C²:|z₁|²+|z₂|p<1} (0 < p < 1). Then, B_2,p (0 < p < 1) is a non-convex complex ellipsoid in C² without smooth boundary. In this article, we establish a boundary Schwarz lemma at z₀ ∈ ∂B_2,p for holomorphic self-mappings of the non-convex complex ellipsoid B_2,p, where z₀ is any smooth boundary point of B_2,p.

关键词: Boundary Schwarz lemma, Holomorphic mappings, Kobayashi metric, non-convex complex ellipsoids

Abstract: Let B_2,p:={z∈C²:|z₁|²+|z₂|p<1} (0 < p < 1). Then, B_2,p (0 < p < 1) is a non-convex complex ellipsoid in C² without smooth boundary. In this article, we establish a boundary Schwarz lemma at z₀ ∈ ∂B_2,p for holomorphic self-mappings of the non-convex complex ellipsoid B_2,p, where z₀ is any smooth boundary point of B_2,p.

Key words: Boundary Schwarz lemma, Holomorphic mappings, Kobayashi metric, non-convex complex ellipsoids

中图分类号:

32F45

何乐, 涂振汉. THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS[J]. 数学物理学报(英文版), 2019, 39(4): 915-926.

Le HE, Zhenhan TU. THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS[J]. Acta mathematica scientia,Series B, 2019, 39(4): 915-926.

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THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS

THE SCHWARZ LEMMA AT THE BOUNDARY OF THE NON-CONVEX COMPLEX ELLIPSOIDS

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