Zihui Zhao, University of Washington
-
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
.