Displaying similar documents to “Properties of distance functions on convex surfaces and applications”

On the points of non-differentiability of convex functions

David Pavlica (2004)

Commentationes Mathematicae Universitatis Carolinae

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We characterize sets of non-differentiability points of convex functions on ℝ n . This completes (in ℝ n ) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.

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...