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arXiv · 1701.08577

Nonsymmetric conical upper density and $k$-porosity

Antti Käenmäki·Ville Suomala
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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.

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Antti Käenmäki, Ville Suomala. 2017-01-30. Nonsymmetric conical upper density and $k$-porosity. https://doi.org/10.1090/s0002-9947-2010-04869-x

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