Properties of fixed point sets and a characterization of the ball in Cn
Fridman, Buma L. Ma, Daowei
Fridman, Buma L.
Ma, Daowei
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2007-01
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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
Abstract
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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American Mathematical Society
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Proceedings of the American Mathematical Society;v.135 no.1
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0002-9939
1088-6826
1088-6826