" Harmonic Measures for Infinitely Connected Domains"
Abstract: In the last 30 years, a series of amazing discoveries about harmonic measure has been made. One of the most important results is Makarov's theorem that harmonic measure on any simply connected domain is singular to α-dimensional Hausdorff measure for α>1 but absolutely continuous to α-dimensional Hausdorff measure if α<1. We talk about the concepts of harmonic measure, Hausdorff measures and equilibrium measures first. Then, we discuss realations between Hausdorff measures and harmonic measure for some infinitely connected domain.
Date: Tuesday, November 26, 2013
Place: Mathematics Seminar Room, SA-141
Tea and cookies will be served before the seminar.