October 31, 2017 @ 3:30 pm – 4:30 pm
Title : Harmonic functions on Sierpinski carpets
Abstract : I will discuss a notion of Sobolev spaces and harmonic functions on Sierpinski carpets, which differs from the classical approach of potential theory in metric measure spaces. The goal is to define a notion that takes into account also the ambient space, where the carpet lives. As an application of carpet-harmonic functions we obtain a quasisymmetric uniformization result for Sierpinski carpets.