English

Asymptotically sharp dimension estimates for $k$-porous sets

Classical Analysis and ODEs 2017-01-31 v1

Abstract

In Rn\mathbb{R}^n, we establish an asymptotically sharp upper bound for the upper Minkowski dimension of kk-porous sets having holes of certain size near every point in kk orthogonal directions at all small scales. This bound tends to nkn-k as kk-porosity tends to its maximum value.

Keywords

Cite

@article{arxiv.1701.08584,
  title  = {Asymptotically sharp dimension estimates for $k$-porous sets},
  author = {Esa Järvenpää and Maarit Järvenpää and Antti Käenmäki and Ville Suomala},
  journal= {arXiv preprint arXiv:1701.08584},
  year   = {2017}
}
R2 v1 2026-06-22T18:03:57.504Z