Zihui Zhao, University of Washington
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PDL C-401
Given a bounded domain 
, the harmonic measure 
is a probability measure on 
and it characterizes where a Brownian traveller in is likely to exit the domain from. The elliptic measure is a non-homogenous variant of harmonic measure.
, the harmonic measure is a probability measure on and it characterizes where a Brownian traveller in 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 and the surface measure 
of the boundary. In particular, are and 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 and .
and the surface measure of the boundary. In particular, are and 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 and .