Properties of fixed point sets and a characterization of the ball in Cn
Fridman, Buma L.
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Buma L. Fridman and Daowei Ma. Properties of Fixed Point Sets and a Characterization of the Ball in Cn. -- Proceedings of the American Mathematical Society , Vol. 135, No. 1 (Jan., 2007), pp. 229-236
We study the fixed point sets of holomorphic selfmaps 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.
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