2006•Chinese Annals of MathematicsRequires access

A Note on Rigidity of Proper Holomorphic Self-mappings

Zhihua Chen

Abstract

The rigidity of proper holomorphic self-mappings on some kinds of generalized Hartogs triangle is proved, i.e., any proper holomorphic self-mapping on the domain of this kind must be an automorphism. The group of its automorphisms is completely characterized. At the same time, the classifications of its automorphisms and proper holomorphic mappings between two domains of this kind are also obtained.

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Key concepts: Holomorphic function, Automorphism, Rigidity (electromagnetism), Mathematics, Pure mathematics, Automorphism group, Identity theorem, Domain (mathematical analysis)