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arXiv · 2006.04303

A characterization of sets in $\mathbb{R}^2$ with DC distance function

Dušan Pokorný·Luděk Zajíček
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Abstract

We give a complete characterization of closed sets $F \subset \mathbb{R}^2$ whose distance function $d_F:= \mathrm{dist}(\cdot,F)$ is DC (i.e., is the difference of two convex functions on $\mathbb{R}^2$). Using this characterization, a number of properties of such sets is proved.

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Dušan Pokorný, Luděk Zajíček. 2020-06-08. A characterization of sets in $\mathbb{R}^2$ with DC distance function. https://arxiv.org/abs/2006.04303

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