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arXiv · 2009.11441

Minimal Riesz energy on balanced fractal sets

Austin Anderson·Alexander Reznikov
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Abstract

We investigate the asymptotic behavior of minimal $N$-point Riesz $s$-energy on fractal sets of non-integer dimension, with algebraically dependent contraction ratios. For $s$ bigger than the dimension of the set $A$, we prove the asymptotic behavior of the minimal $N$-point Riesz $s$-energy of $A$ along explicit subsequences, but we show that the general asymptotic behavior does not exist.

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Austin Anderson, Alexander Reznikov. 2020-09-24. Minimal Riesz energy on balanced fractal sets. https://arxiv.org/abs/2009.11441

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