Harmonic measure and Hausdorff measures

Abstract

Understanding the geometric and metric properties of harmonic measure is important for the solution of the Dirichlet problem for the Laplacian. In this talk I will survey the results obtained in recent years regarding the connection between harmonic measure, Hausdorff measures, and rectifiability, which plays a prominent role in the codimension 1 case. I will also review some open questions and partial results in other codimensions, where the situation is not well understood.