English

Nonsymmetric conical upper density and $k$-porosity

Classical Analysis and ODEs 2017-01-31 v1

Abstract

We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in Rn\mathbb{R}^n. As an application, we find an upper bound close to nkn-k for the Hausdorff dimension of sets with large kk-porosity. With kk-porous sets we mean sets which have holes in kk different directions on every small scale.

Keywords

Cite

@article{arxiv.1701.08577,
  title  = {Nonsymmetric conical upper density and $k$-porosity},
  author = {Antti Käenmäki and Ville Suomala},
  journal= {arXiv preprint arXiv:1701.08577},
  year   = {2017}
}
R2 v1 2026-06-22T18:03:56.404Z