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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Common fixed points in hyperbolic Riemann surfaces and convex domains
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by Marco Abate and Jean-Pierre Vigué PDF
Proc. Amer. Math. Soc. 112 (1991), 503-512 Request permission

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.
References
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 503-512
  • MSC: Primary 32H50; Secondary 30F10, 58C30
  • DOI: https://doi.org/10.1090/S0002-9939-1991-1065938-8
  • MathSciNet review: 1065938