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Extremal Problems for Convex Curves with a Given Self Chebyshev Radius

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Abstract

The paper is devoted to some extremal problems for convex curves and polygons in the Euclidean plane referring to the self Chebyshev radius. In particular, we determine the self Chebyshev radius for the boundary of an arbitrary triangle. Moreover, we derive the maximal possible perimeter for convex curves and boundaries of convex n-gons with a given self Chebyshev radius.

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Acknowledgements

The authors are grateful to the referee for helpful comments and suggestions that improved the presentation of this paper.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade Federal Fluminense, 24210201, Niterói, Brazil

    Vitor Balestro

  2. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Horst Martini

  3. Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Markus st., 22, Vladikavkaz, Russia, 362027

    Yurii Nikonorov

  4. Volgodonsk Engineering Technical Institute the branch of National Research Nuclear University “MEPhI”, Lenin st., 73/94, Volgodonsk, Russia, 347360

    Yulia Nikonorova

Authors
  1. Vitor Balestro
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  2. Horst Martini
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  3. Yurii Nikonorov
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  4. Yulia Nikonorova
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Correspondence to Vitor Balestro.

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Balestro, V., Martini, H., Nikonorov, Y. et al. Extremal Problems for Convex Curves with a Given Self Chebyshev Radius. Results Math 76, 87 (2021). https://doi.org/10.1007/s00025-021-01394-6

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  • DOI: https://doi.org/10.1007/s00025-021-01394-6

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