Minimal Riesz energy on balanced fractal sets
Classical Analysis and ODEs
2020-09-25 v1 Metric Geometry
Abstract
We investigate the asymptotic behavior of minimal -point Riesz -energy on fractal sets of non-integer dimension, with algebraically dependent contraction ratios. For bigger than the dimension of the set , we prove the asymptotic behavior of the minimal -point Riesz -energy of along explicit subsequences, but we show that the general asymptotic behavior does not exist.
Keywords
Cite
@article{arxiv.2009.11441,
title = {Minimal Riesz energy on balanced fractal sets},
author = {Austin Anderson and Alexander Reznikov},
journal= {arXiv preprint arXiv:2009.11441},
year = {2020}
}