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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Points fixes d'applications holomorphes dans un domaine borné convexe de $ {\bf C}\sp n$


Author: Jean-Pierre Vigué
Journal: Trans. Amer. Math. Soc. 289 (1985), 345-353
MSC: Primary 32H15; Secondary 58C30
MathSciNet review: 779068
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Abstract: Let $ D$ be a bounded convex domain in $ {{\mathbf{C}}^n}$. We prove that the set $ V$ of fixed points of a holomorphic map $ f:D \to D$ is a complex submanifold of $ D$ and, if $ V$ is not empty, $ V$ is a holomorphic retract of $ D$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0779068-5
PII: S 0002-9947(1985)0779068-5
Keywords: Points fixes d'une application holomorphe, distances invariantes
Article copyright: © Copyright 1985 American Mathematical Society