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 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.
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}
}