Geodesic
A characterization of sets in ${\mathbb R}^2$ with DC distance function
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 1-38.

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We give a complete characterization of closed sets $F \subset {\mathbb R}^2$ whose distance function $d_F:= {\rm dist}(\cdot ,F)$ 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.
DOI : 10.21136/CMJ.2021.0228-20
Classification : 26B25
Keywords: distance function; DC function; subset of ${\mathbb R}^2$ 
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Pokorný, Dušan; Zajíček, Luděk. A characterization of sets in ${\mathbb R}^2$ with DC distance function. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 1, pp. 1-38. doi : 10.21136/CMJ.2021.0228-20. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2021.0228-20/

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