Tame nonsmooth inverse mapping theorems
Toshizumi Fukui, Krzysztof Kurdyka (LM-Savoie), Laurentiu Paunescu
TL;DR
This paper develops local and global inverse mapping theorems for tame, possibly nonsmooth, mappings that are definable in o-minimal structures, using properties of Jacobian matrices.
Contribution
It introduces new inverse mapping theorems for tame, nonsmooth mappings based on properties of Jacobian matrices within o-minimal structures.
Findings
Established inverse theorems for tame mappings with convexity and positivity conditions.
Provided conditions for invertibility in local and global contexts.
Extended classical inverse theorems to nonsmooth, tame settings.
Abstract
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.