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arXiv · 2103.07685

Uniqueness of centers of nearly spherical bodies

Jun O'Hara
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Abstract

An $r^{\an}$-center of a compact body $\Om$ in an $n$ dimensional Euclidean space is a point that gives an extremal value of the regularized Riesz potential, which is the (Hadamard regularization of) integration on $\Om$ of the distance from the point to the power $\an$. We show that for any real number $\la$ if a compact body is sufficiently close to a ball in the sense of asphericity then the $r^{\an}$-center is unique. We also study the regularized potentials of a unit ball.

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Jun O'Hara. 2021-03-13. Uniqueness of centers of nearly spherical bodies. https://arxiv.org/abs/2103.07685

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