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

 

Common fixed points in hyperbolic Riemann surfaces and convex domains


Authors: Marco Abate and Jean-Pierre Vigué
Journal: Proc. Amer. Math. Soc. 112 (1991), 503-512
MSC: Primary 32H50; Secondary 30F10, 58C30
MathSciNet review: 1065938
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Abstract: In this paper we prove that a commuting family of continuous self-maps of a bounded convex domain in $ {\mathbb{C}^n}$ which are holomorphic in the interior has a common fixed point. The proof makes use of three basic ingredients: iteration theory of holomorphic maps, a precise description of the structure of the boundary of a convex domain, and a similar result for commuting families of self-maps of a hyperbolic domain of a compact Riemann surface.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1065938-8
PII: S 0002-9939(1991)1065938-8
Article copyright: © Copyright 1991 American Mathematical Society