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Experimental investigation on the uniqueness of a center of a body

Volume 118 / 2016

Shigehiro Sakata Annales Polonici Mathematici 118 (2016), 149-171 MSC: Primary 52A40, 52A10, 52A20, 51M16; Secondary 35B38, 26B25. DOI: 10.4064/ap4047-12-2016 Published online: 9 January 2017


The object of our investigation is a point that gives the maximum value of a potential with a strictly decreasing radially symmetric kernel. It defines a center of a body in $\mathbb {R}^m$. When the kernel is the Riesz kernel or the Poisson kernel, such a center is called an $r^{\alpha -m}$-center or an illuminating center, respectively.

The existence of a center is easily shown but uniqueness does not always hold. The main results in this paper are some new sufficient conditions for the uniqueness.


  • Shigehiro SakataFaculty of Education
    University of Miyazaki
    1-1 Gakuen Kibanadai West
    Miyazaki, 889-2192, Japan

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