English

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

Functional Analysis 2013-03-12 v1

Abstract

We construct a Lipschitz function on \er2\er^{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

Cite

@article{arxiv.1303.2594,
  title  = {Nonconvex Lipschitz function in plane which is locally convex outside a discontinuum},
  author = {Dusan Pokorny},
  journal= {arXiv preprint arXiv:1303.2594},
  year   = {2013}
}
R2 v1 2026-06-21T23:40:07.664Z