Global inversion and covering maps on length spaces
type: Item
instance of: scholarly article
title: Global inversion and covering maps on length spaces
zbMATH Open document ID: 1198.58004
author: Olivia Gutú
author: M. I. Garrido
author: Jesús A. Jaramillo
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-07-13T00:00:00Z
review text: This is an interesting paper on some global inversion results for length metric spaces. In Section 2, the authors obtain in terms of liftings of rectifiable paths, a fairly general characterization of covering maps of length spaces (Theorem 3). In Section 3, they give an estimate of the domain of invertibility of a local homeomorphism around a given point in terms of the lower scalar derivative (Theorem 6). In Section 4, some applications of these results are given to the case of local diffeomorphisms between Finsler manifolds (Theorem 11). The last section contains a global inversion theorem for mappings between stratified groups (Theorem 14). Papers by the second author directly connected to this topic are [Math. Ann. 338, No.~1, 75--95 (2007; Zbl 1115.58006)] (with \textit{J. A. Jaramillo}) and [Nonlinear Anal., Theory Methods Appl. 66, No.~12 (A), 2688--2697 (2007; Zbl 1123.58005)].
reviewed by: Dorin Andrica
Mathematics Subject Classification ID: 58C15
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 54E40
zbMATH DE Number: 5736455
zbMATH Keywords: global inversion
zbMATH Keywords: length spaces
zbMATH Keywords: covering maps
zbMATH Keywords: Banach-Finsler manifold
zbMATH Keywords: stratified group
MaRDI profile type: Publication
full work available at URL: j.na.2010.04.069
OpenAlex ID: W2039967091
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DOI: 10.1016/J.NA.2010.04.069
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description: scientific article; zbMATH DE number 5736455