Metric regularity, pseudo-jacobians and global inversion theorems on Finsler manifols

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Gutú, Olivia and Jaramillo Aguado, Jesús Ángel and Madiedo Castro, Óscar Reynaldo (2022) Metric regularity, pseudo-jacobians and global inversion theorems on Finsler manifols. (Unpublished)

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Abstract

Our aim in this paper is to study the global invertibility of a locally Lipschitz map f : X → Y between (possibly infinite-dimensional) Finsler manifolds, stressing the connections with covering properties and metric regularity of f. To this end, we introduce a natural notion of pseudo-Jacobian Jf in this setting, as is a kind of set-valued differential object associated to f. By means of a suitable index, we study the relations between properties of pseudo-Jacobian Jf and local metric properties of the map f, which lead to conditions for f to be a covering map, and for f to be globally invertible. In particular, we obtain a version of Hadamard integral condition in this context.


Item Type:Article
Uncontrolled Keywords:Global invertibility; Finsler manifolds; Nonsmooth analysis
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:73512
Deposited On:11 Jul 2022 16:00
Last Modified:02 Aug 2022 08:28

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