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arXiv · 0812.2387

Dimension of elliptic harmonic measure of Snowspheres

Daniel Meyer
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Abstract

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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Daniel Meyer. 2010-02-26. Dimension of elliptic harmonic measure of Snowspheres. https://arxiv.org/abs/0812.2387

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