Global inversion and covering maps on length spaces
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)].
scientific article; zbMATH DE number 5736455
scientific article