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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|