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Geometric Structure of Chebyshev Sets and Suns in Three-Dimensional Spaces with a Cylindrical Norm

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Moscow University Mathematics Bulletin Aims and scope

Abstract

A geometric characterization of Chebyshev sets and suns in three-dimensional polyhedral spaces with cylindrical norm is presented. A number of new properties of Chebyshev sets, suns, sets with continuous metric projection in three-dimensional spaces is put forward. The new recent fact established by A. R. Alimov and E. V. Shchepin that suns and Chebyshev sets are convex in tangent directions to the unit sphere plays an important role in the paper.

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ACKNOWLEDGMENTS

The author thanks I. G. Tsar’kov and P. A. Borodin for helpful discussions.

Funding

The work is supported by the Russian Foundation for Basic Research (projects nos. 18-01-00333-a and 19-01-00332-a).

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Authors and Affiliations

  1. Laboratory of Computational Methods, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 119234, Moscow, Russia

    A. R. Alimov

  2. Steklov Mathematical Institute, Russian Academy of Sciences, 117966, Moscow, Russia

    A. R. Alimov

  3. Moscow Center for Fundamental and Applied Mathematics, 119234, Moscow, Russia

    A. R. Alimov

Authors
  1. A. R. Alimov
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Correspondence to A. R. Alimov.

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The authors declare that they have no conflicts of interest.

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Translated by E. Oborin

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Alimov, A.R. Geometric Structure of Chebyshev Sets and Suns in Three-Dimensional Spaces with a Cylindrical Norm. Moscow Univ. Math. Bull. 75, 209–215 (2020). https://doi.org/10.3103/S0027132220050022

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  • DOI: https://doi.org/10.3103/S0027132220050022

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