Dimension of elliptic harmonic measure of Snowspheres

Details Dimension of elliptic harmonic measure of Snowspheres Dimension of elliptic harmonic measure of Snowspheres

2008-12-12

arxiv.org/abs/0812.2387v3

Illinois Journal of Mathematics, Vol. 53, No. 2, (2009) 691-721

Mathematics

Complex Variables

33 pages, 1 figure

Scientific paper

A metric space $\mathcal{S}$ is called a \defn{quasisphere} if there is a quasisymmetric homeomorphism $f\colon S^2\to \mathcal{S}$. We consider the elliptic harmonic measure, i.e., the push forward of 2-dimensional Lebesgue measure by $f$. It is shown that for certain self similar quasispheres $\mathcal{S}$ (snowspheres) the dimension of the elliptic harmonic measure is strictly less than the Hausdorff dimension of $\mathcal{S}$.

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