Median porosity is quasiconformally invariant

Abstract

A set in $\mathbb{R}^n$ is median porous if the logarithm of its distance function has bounded mean oscillation. We show that this property is preserved under quasiconformal mappings. In particular, median porosity is quasiconformally invariant. We also show that the stronger notion of weak porosity, by contrast, is not quasiconformally invariant.