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A Boundary Rigidity Problem For Holomorphic Mappings on Some Weakly Pseudoconvex Domains

Published online by Cambridge University Press:  20 November 2018

Xiaojun Huang
Xiaojun Huang*
Affiliation:
Department of Mathematics Washington University St. Louis, Missouri 63130 U.S.A e–mail: c31995xh@wuvmd.wustl.edu
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Abstract

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In this paper, we study the boundary version of the classical Cartan theorem. We show that for some weakly pseudoconvex domains, when a holomorphic self-mapping has a sufficiently high order of contact (which depends only on the geometric properties of the domains) with the identical map at some boundary point, then it must coincide with the identity.

Keywords

32H0232H15Burns-Krantz rigidity problemsiteration of self-mappingsKobayashi metrics and Kobayashi distancescomplex geodesiesholomorphic retractshorospherespseudoconvex domains of finite type.
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 2 , 01 April 1995 , pp. 405 - 420
Copyright
Copyright © Canadian Mathematical Society 1995

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