Global inversion of nonsmooth mappings on Finsler manifolds

2012/01/23 by Jesus A. Jaramillo, Jaramillo, Jesus A., Oscar Madiedo +3
Mathematics · #49J52 #58C15 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #math.DG #math.FA #msc:49J52 #msc:58C15

paper · pdf · doi:10.48550/arxiv.1201.4666

18 pages

arxiv created 2012/01/23 · arxiv updated 2012/01/24

Abstract

We consider the problem of finding sufficient conditions for a locally Lipschitz mapping between Finsler manifolds to be a global homeomorphism. For this purpose, we develop the notion of Clarke generalized differential in this context and, using this, we obtain a version of the Hadamard integral condition for invertibility. As consequences, we deduce some global inversion and global injectivity results for Lipschitz mappings on ℝⁿ in terms of spectral conditions of its Clarke generalized differential.

Related

• Metric regularity, pseudo-Jacobians and global inversion theorems on Finsler manifolds
• Global inversion of nonsmooth mappings using pseudo-Jacobian matrices
• On some generalizations of Hadamard's inversion theorem beyond differentiability
• A sufficient condition for global invertibility of Lipschitz mapping
• A note on a global invertibility of locally lipschitz functions on Rⁿ