Experimental investigation on the uniqueness of a center of a body
Volume 118 / 2016
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
Abstract
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.
