The Schwarz lemma at the boundary of the symmetrized bidisc

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Tu, Zhenhan¹  Zhang, Shuo¹ 

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

关键词: Boundary Schwarz lemma;    Caratheodory metric;    Holomorphic mappings;    Symmetrized bidisc;   

DOI  :  10.1016/j.jmaa.2017.10.061

来源: Elsevier

【 摘 要 】

Y The symmetrized bidisc G2 is defined by G(2) := {(z(1) + z(2), z(1)z(2)) is an element of C-2 : vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar < 1, z(1), z(2) is an element of C}. It is a bounded inhomogeneous pseudoconvex domain without Cl boundary, and especially the symmetrized bidisc hasn't any strongly pseudoconvex boundary point and the boundary behavior of both Caratheodory and Kobayashi metrics over the symmetrized bidisc is hard to describe precisely. In this paper, we study the boundary Schwarz lemma for holomorphic self-mappings of the symmetrized bidisc G2, and our boundary Schwarz lemma in the paper differs greatly from the earlier related results. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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