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

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.