Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum

2013/03/08 by Dušan Pokorný, Pokorny, Dusan
Mathematics · Computer Science · #Functional Equations Stability Results #Advanced Banach Space Theory #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1303.2594

Abstract

We construct a Lipschitz function on \er² which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and was also cited by other authors.

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