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

• 论文 •    下一篇

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

何乐, 涂振汉   

  1. 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   

  1. 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: Let B2,p:={z∈C2:|z1|2+|z2|p<1} (0 < p < 1). Then, B2,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 ∈ ∂B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2,p, where z0 is any smooth boundary point of B2,p.

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

Abstract: Let B2,p:={z∈C2:|z1|2+|z2|p<1} (0 < p < 1). Then, B2,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 ∈ ∂B2,p for holomorphic self-mappings of the non-convex complex ellipsoid B2,p, where z0 is any smooth boundary point of B2,p.

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

中图分类号: 

  • 32F45