Fixed points and uniqueness of complex geodesics
type: Item
instance of: scholarly article
title: Fixed points and uniqueness of complex geodesics
zbMATH Open document ID: 0763.53045
DOI: 10.1007/BF02844690
author: Chiara de Fabritiis
publication date: 1992-09-27T00:00:00Z
review text: Let \(V\) be a bounded circular domain in \(\mathbb{C}^ n\) and let \(f\) be in the space of all holomorphic mappings from \(V\) to \(V\); if 0 and \(x\) are fixed points of \(f\), then the existence of a complex geodesic whose range contains 0 and \(x\) and is contained in the set fix\(f=\{Z\in V:f(Z)=Z\}\) is ensured in \textit{J.-P. Vigue}'s papers [Adv. Math. 52, 241-247 (1984; Zbl 0555.32015) and Trans. Am. Math. Soc. 289, 345-353 (1985; Zbl 0589.32043)]. The main result shows that the uniqueness of such a geodesic is equivalent to the condition of the intersection between fix\(f\) and the set which describes the behaviour of the boundary of \(V\) in the direction of \(x\).
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 60571
zbMATH Keywords: bounded circular domain
zbMATH Keywords: holomorphic mappings
zbMATH Keywords: complex geodesic
reviewed by: Cornelia-Livia Bejan
MaRDI profile type: Publication
cites work: Common Fixed Points in Hyperbolic Riemann Surfaces and Convex Domains
cites work: Q3892778
cites work: Q4045220
cites work: Halbräume und ihre holomorphen Automorphismen
cites work: Q5608188
cites work: Intrinsic distances, measures and geometric function theory
cites work: Q5658761
cites work: Points fixes d'une application holomorphe d'un domaine borné dans lui- même. (Fixed points of a holomorphic mapping of a bounded domain into itself)
cites work: Q4201299
cites work: Q3949259
cites work: Q4743072
cites work: Géodésiques complexes et points fixes d'applications holomorphes
cites work: Points Fixes D'Applications Holomorphes Dans Un Domaine Borne Convexe De C n
cites work: Q5682591
full work available at URL: https://doi.org/10.1007/bf02844690
OpenAlex ID: W2082842561
published in: Rendiconti del Circolo Matematico di Palermo
Recommended article: Q3814018
Recommended article: Uniqueness of complex geodesics and characterization of circular domains
Recommended article: Q3979710
Recommended article: Q3778481
Recommended article: Q4462019
Recommended article: Q4838357
Recommended article: Complex Geodesics on Convex Domains
Recommended article: Q3749327
Recommended article: Q4882747
Recommended article: Q4347750
description: scientific article; zbMATH DE number 60571