We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in 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.
@article{bwmeta1.element.bwnjournal-article-apmv56z2p143bwm,
author = {Do Duc Thai},
title = {The fixed points of holomorphic maps on a convex domain},
journal = {Annales Polonici Mathematici},
volume = {57},
year = {1992},
pages = {143-148},
zbl = {0761.32012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv56z2p143bwm}
}
Do Duc Thai. The fixed points of holomorphic maps on a convex domain. Annales Polonici Mathematici, Tome 57 (1992) pp. 143-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z2p143bwm/
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