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A characterization of sets in ℝ2 with DC distance function

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Abstract

We give a complete characterization of closed sets F ⊂ ℝ2 whose distance function dF:= dist(·, F) is DC (i.e., is the difference of two convex functions on ℝ2). Using this characterization, a number of properties of such sets is proved.

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Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czech Republic

    Dušan Pokorný & Luděk Zajíček

Authors
  1. Dušan Pokorný
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  2. Luděk Zajíček
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Corresponding author

Correspondence to Dušan Pokorný.

Additional information

The research was supported by GAČR 18-11058S.

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Pokorný, D., Zajíček, L. A characterization of sets in ℝ2 with DC distance function. Czech Math J 72, 1–38 (2022). https://doi.org/10.21136/CMJ.2021.0228-20

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  • DOI: https://doi.org/10.21136/CMJ.2021.0228-20

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