Partial Differential Equations seminar
Speaker: Aritro Pathak, visiting fellow, TIFR Mumbai
Host: Harsha Hutridurga
Title: Uniform domains with Ahlfors-David regular boundaries, and uniform rectifiability.
Time, day and date: 11:30:00 AM – 12:30:00 PM, Wednesday, August 19
Venue: Ramanujan Hall
Abstract: Uniform rectifiability is a quantitative notion of rectifiability that is closely related to the (L^2) boundedness of Riesz transforms. Uniform domains satisfy quantitative openness and quantitative path connectivity conditions. When the Ahlfors-David regular boundary of a uniform domain is uniformly rectifiable, one obtains solvability of the Dirichlet problem for the Laplacian with rough boundary data, as well as quantitative absolute continuity of harmonic measure. We will discuss some recent results in this active area at the interface of geometric measure theory and harmonic analysis. In particular, we will present a new result concerning the Weak Geometric Lemma and uniform rectifiability for Ahlfors-David regular sets whose complements are uniform domains.