Acta Mathematica Scientia

, Volume 39, Issue 4, pp 915–926 | Cite as

The Schwarz Lemma at the Boundary of the Non-Convex Complex Ellipsoids

  • Le He (何乐)
  • Zhenhan Tu (涂振汊)Email author


Let B2,p:= {z ∈ ℂ2: ∣z12+ ∣z2p < 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 

2010 MR Subject Classification

32F45 32H02 30C80 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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