# Elliptic measures and the geometry of the domains

Zihui Zhao, University of Washington
Tuesday, May 1, 2018 - 1:30pm to 3:30pm
PDL C-401
Given a bounded domain $\Omega$, the harmonic measure $\omega$ is a probability measure on $\partial\Omega$and it characterizes where a Brownian traveller in $\Omega$ is likely to exit the domain from. The elliptic measure is a non-homogenous variant of harmonic measure.
Since 1917, there has been much study about the relationship between the elliptic/harmonic measure $\omega$ and the surface measure $\sigma$ of the boundary. In particular, are $\omega$ and $\sigma$ absolutely continuous with each other? In this talk, I will show how a positive answer to this question implies that the corresponding domain enjoys good geometric property, thus we obtain a sufficient condition for the absolute continuity of $\omega$ and $\sigma$.

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