Proceedings of the American Mathematical Society

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

Author(s): Buma L. Fridman; Daowei Ma
Journal: Proc. Amer. Math. Soc. 135 (2007), 229-236.
MSC (2000): Primary 32M05, 54H15
Posted: June 29, 2006
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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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Buma L. Fridman
Affiliation: Department of Mathematics, Wichita State University, Wichita, Kansas 67260-0033
Email: buma.fridman@wichita.edu

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