[Seminar] Poincare inequalities on the Vicsek set, Professor Chen Li, Louisiana State University

Abstract:

The Vicsek set is a tree-like fractal on which neither analog of curvature nor differential structure exists, whereas the heat kernel satisfies sub-Gaussian estimates. I will talk about Sobolev spaces and scale invariant \(L^p\) Poincar\'e inequalities on the Vicsek set. Several approaches will be discussed, including the metric approach of Korevaar-Schoen and the approach by limit approximation of discrete p-energies.

Zoom: https://oist.zoom.us/meeting/register/tJEpdu-uqTwrGdFV5IrA0woMhvhlxVa_5ttw