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A generalization of domains of constant width

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Abstract

Recently, Ou and Pan introduced the higher order width functions of convex domains, and posed a generalization of the Blaschke–Lebesgue problem: among all convex domains having constant \(k\)-order width, which has the least possible area. In this paper, we continue to study convex domains having constant \(k\)-order width and obtain some characterizations of this class of sets, which are slightly different from those of constant width convex domains.

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Acknowledgments

The author would like to thank referees for their careful reading of the manuscript of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China

    Deyan Zhang

  2. College of mathematics and statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Deyan Zhang

Authors
  1. Deyan Zhang
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Corresponding author

Correspondence to Deyan Zhang.

Additional information

This work was completed with the support of the National Natural Science Foundation of China (No. 11161019).

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Zhang, D. A generalization of domains of constant width. Beitr Algebra Geom 57, 259–270 (2016). https://doi.org/10.1007/s13366-015-0252-8

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  • DOI: https://doi.org/10.1007/s13366-015-0252-8

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