Given a bounded domain $\Omega$, the harmonic measure $\omega$ is a probability measure on $\partial \Omega$ and it characterizes where a Brownian traveller moving 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 harmonic/elliptic 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 $\sigma$.

# Analysis Seminar

## Elliptic measures and the geometry of domains

### Featuring

Zihui Zhao

### Speaker Affiliation

Member, School of Mathematics

### Affiliation

Mathematics

### Event Series

### Video

https://video.ias.edu/analysis/2019/0214-ZihuiZhaoDate & Time

February 14, 2019 | 1:00 – 2:00pm

### Location

Simonyi Hall 101