Nonsymmetric conical upper density and 𝑘-porosity

Author:

Käenmäki Antti,Suomala Ville

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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