Properties of fixed point sets and a characterization of the ball in ℂn


Journal Article

We study the fixed point sets of holomorphic self-maps of a bounded domain in ℂn. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be the identity. We have discovered that in terms of this number one can give the necessary and sufficient condition for the domain to be biholomorphic to the unit ball. Other theorems and examples generalize and complement previous results in this area, especially the recent work of Jean-Pierre Vigué. © 2006 American Mathematical Society.

Full Text

Cited Authors

  • Fridman, BL; Ma, D

Published Date

  • January 1, 2007

Published In

Volume / Issue

  • 135 / 1

Start / End Page

  • 229 - 236

International Standard Serial Number (ISSN)

  • 0002-9939

Digital Object Identifier (DOI)

  • 10.1090/S0002-9939-06-08641-2

Citation Source

  • Scopus