Points fixes d’applications holomorphes dans un domaine borné convexe de 𝐶ⁿ

Vigué, Jean-Pierre

doi:10.1090/S0002-9947-1985-0779068-5

Points fixes d’applications holomorphes dans un domaine borné convexe de $\textbf {C}^ n$
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Trans. Amer. Math. Soc. 289 (1985), 345-353 Request permission

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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