Czechoslovak Mathematical Journal, Vol. 72, No. 1, pp. 1-38, 2022
A characterization of sets in ${\mathbb R}^2$ with DC distance function
Dušan Pokorný, Luděk Zajíček
Received June 4, 2020. Published online July 15, 2021.
Abstract: 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.
Keywords: distance function; DC function; subset of ${\mathbb R}^2$
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Affiliations: Dušan Pokorný (corresponding author), Luděk Zajíček, Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Prague 8, Czech Republic, e-mail: dpokorny@karlin.mff.cuni.cz, zajicek@karlin.mff.cuni.cz
