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

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 i...

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Detalles Bibliográficos
Autores: Gutú, Olivia, Jaramillo Aguado, Jesús Ángel, Madiedo Castro, Óscar Reynaldo
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71789
Acceso en línea:https://hdl.handle.net/20.500.14352/71789
Access Level:acceso abierto
Palabra clave:517.988
Global invertibility
Finsler manifolds
Nonsmooth analysis
Análisis funcional y teoría de operadores
Descripción
Sumario: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.