Cole Jeznach, University of Minnesota

PDL C401
The relationship between harmonic measure and surface measure of a domain is largely connected with the geometry of the domain itself. In many fractals (for example, in domains with relatively "large'' boundaries, and outside selfsimilar "enough'' Cantor sets), these measures are mutually singular, and in fact, have different dimensions. After recalling some of these results I will present joint work with G. David and A. Julia where we demonstrate examples where the exact opposite occurs: we construct Cantortype sets in the plane that are Ahlfors regular (of small dimension) for which their associated harmonic measure and surface measure are bounded equivalent.