Rigidity of proper holomorphic mappings between certain unbounded non-hyperbolic domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:419

Article

Tu, Zhenhan¹  Wang, Lei¹ 

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

关键词: Fock-Bargmann-Hartogs domains;    Proper holomorphic mappings;    Unbounded circular domains;   

DOI  :  10.1016/j.jmaa.2014.04.073

来源: Elsevier

【 摘 要 】

The Fock-Bargmann-Hartogs domain D-n,D-m(mu) (mu > 0) in Cn+m is defined by the inequality parallel to w parallel to(2) < e(-mu parallel to z parallel to 2), where (z, w) is an element of C-n x C-m, which is an unbounded non-hyperbolic domain in Cn+m. Recently, Yamamori gave an explicit formula for the Bergman kernel of the Fock-Bargmann-Hartogs domains in terms of the polylogarithm functions and Kim-Ninh-Yamarnori determined the automorphism group of the domain D-n,D-m(mu). In this article, we obtain rigidity results on proper holomorphic mappings between two equidimensional Fock-Bargmann-Hartogs domains. Our rigidity result implies that any proper holomorphic self-mapping on the Fock-Bargmann-Hartogs domain Dn fin (it) with m >= 2 must be an automorphism. (C) 2014 Elsevier Inc. All rights reserved.

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