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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Properties of fixed point sets and a characterization of the ball in $ {\mathbb{C}}^n$


Authors: Buma L. Fridman and Daowei Ma
Journal: Proc. Amer. Math. Soc. 135 (2007), 229-236
MSC (2000): Primary 32M05, 54H15
Published electronically: June 29, 2006
MathSciNet review: 2280191
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Abstract: We study the fixed point sets of holomorphic self-maps of a bounded domain in $ {\mathbb{C}}^n$. 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.


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Additional Information

Buma L. Fridman
Affiliation: Department of Mathematics, Wichita State University, Wichita, Kansas 67260-0033
Email: buma.fridman@wichita.edu

Daowei Ma
Affiliation: Department of Mathematics, Wichita State University, Wichita, Kansas 67260-0033
Email: dma@math.wichita.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08641-2
PII: S 0002-9939(06)08641-2
Received by editor(s): August 2, 2005
Published electronically: June 29, 2006
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2006 American Mathematical Society