English

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 NN-point Riesz ss-energy on fractal sets of non-integer dimension, with algebraically dependent contraction ratios. For ss bigger than the dimension of the set AA, we prove the asymptotic behavior of the minimal NN-point Riesz ss-energy of AA 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}
}