Tame nonsmooth inverse mapping theorems

Toshizumi Fukui (1) , Krzysztof Kurdyka (2) , Laurentiu Paunescu (3)

1 Department of Mathematics
2 LAMA - Laboratoire de Mathématiques
3 School of Mathematics and statistics [Sydney]

We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity of some principal minors, contractiblity) of the space of Jacobi's matrices at smooth points.

Mots clés: inverse mapping; univalence; convex; subanalytic; o-minimal; Lipschitz

Domaines: Topologie géométrique [math.GT]

Toshizumi Fukui, Krzysztof Kurdyka, Laurentiu Paunescu. Tame nonsmooth inverse mapping theorems. 2007. ⟨hal-00198692⟩