Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (4): 915-926.doi: 10.1007/s10473-019-0401-5

• Articles •     Next Articles

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).

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

CLC Number: 

  • 32F45
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