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Stationary radial centers and symmetry of convex polytopes

Volume 159 / 2020

Shigehiro Sakata Colloquium Mathematicum 159 (2020), 91-106 MSC: Primary 35B38, 52B15; Secondary 52A39, 52A10. DOI: 10.4064/cm7712-11-2018 Published online: 10 October 2019

Abstract

We investigate centers of a body (the closure of a bounded open set) in $\mathbb R ^m$ defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson’s integral. These centers, in general, depend on parameters and vary with the parameters. We give a necessary and sufficient condition for the existence of a center independent of a parameter.

Authors

  • Shigehiro SakataDepartment of Applied Mathematics
    Faculty of Science
    Fukuoka University
    8-19-1 Nanakuma, Jonan ward
    814-0180 Fukuoka, Japan
    e-mail

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