Displaying similar documents to “Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum”

On inverses of δ -convex mappings

Jakub Duda (2001)

Commentationes Mathematicae Universitatis Carolinae

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In the first part of this paper, we prove that in a sense the class of bi-Lipschitz δ -convex mappings, whose inverses are locally δ -convex, is stable under finite-dimensional δ -convex perturbations. In the second part, we construct two δ -convex mappings from ℓ 1 onto ℓ 1 , which are both bi-Lipschitz and their inverses are nowhere locally δ -convex. The second mapping, whose construction is more complicated, has an invertible strict derivative at 0 . These mappings show that for (locally) δ -convex...

Lipschitz sums of convex functions

Marianna Csörnyei, Assaf Naor (2003)

Studia Mathematica

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We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.

Bi-Lipschitz trivialization of the distance function to a stratum of a stratification

Adam Parusiński (2005)

Annales Polonici Mathematici

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Given a Lipschitz stratification 𝒳 that additionally satisfies condition (δ) of Bekka-Trotman (for instance any Lipschitz stratification of a subanalytic set), we show that for every stratum N of 𝒳 the distance function to N is locally bi-Lipschitz trivial along N. The trivialization is obtained by integration of a Lipschitz vector field.