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arXiv · 1810.01557

Riesz energy on self-similar sets

Alexander Reznikov·Oleksandr Vlasiuk
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Abstract

We investigate properties of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, as well as asymptotic behavior of $N$-point configurations that minimize this energy. For $s$ bigger than the dimension of the set $A$, we constructively prove a negative result concerning the asymptotic behavior (namely, its nonexistence) of the minimal $N$-point Riesz $s$-energy of $A$, but we show that the asymptotic exists over reasonable sub-sequences of $N$. Furthermore, we give a short proof of a result concerning asymptotic behavior of configurations that minimize the discrete Riesz $s$-energy.

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Alexander Reznikov, Oleksandr Vlasiuk. 2018-10-03. Riesz energy on self-similar sets. https://arxiv.org/abs/1810.01557

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