Zihui Zhao

PDL C-36

Abstract: 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 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.

This talk is a preparation for my thesis defense!