Zihui Zhao, University of Washington

Tuesday, May 1, 2018 - 1:30pm to 3:30pm

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.

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 .