Nonsymmetric conical upper density and $k$-porosity

Abstract

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

References in corpus (2)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• Conical upper density theorems and porosity of measures

Cited by in corpus (2)

• Packing dimension and Ahlfors regularity of porous sets in metric spaces
• On upper conical density results