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

Comment.Math.Univ.Carolin. 55,4 (2014) 509-521.

Abstract:We construct a Lipschitz function on $\mathbb R^2$ 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.

Keywords: convex function; convex set; exceptional set
AMS Subject Classification: 26B25 52A20