The fixed points of holomorphic maps on a convex domain

Thai Do

ArticleOriginal scientific text

Title

The fixed points of holomorphic maps on a convex domain

Authors ¹

Affiliations

Department of Mathematics, Pedagogical Institute of Ha Noi N°I, Ha Noi, Viet Nam

Abstract

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in

ℂ^{n}

then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

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Title

The fixed points of holomorphic maps on a convex domain

Affiliations

Abstract

Bibliography