The Hausdorff dimension of planar elliptic measures via quasiconformal mappings

Abstract

In this paper we study the dimension of planar elliptic measures via the application of quasiconformal mappings. In fact, in our case studies, we find a quasiconformal mapping that relates the elliptic measure in a domain to the harmonic measure in its image domain, and we deduce bounds for the Hausdorff dimension of the elliptic measure by the known results on the harmonic side.