Talk page
Title:
Densities of measures, tubular neighborhoods, and heat content in the Heisenberg group
Speaker:
Abstract:
I will discuss several recent results in geometric measure theory, metric geometry and analysis in the sub-Riemannian Heisenberg group, specifically, Marstrand and Preiss Density Theorems for the Korányi metric, a classification of uniform measures in the first Heisenberg group, and volumes of tubular Carnot-Carathéodory neighborhoods and heat content asymptotics for smoothly bounded domains with noncharacteristic boundary. A unifying theme in these results is the role of the intrinsically sub-Riemannian differential geometry of curves and surfaces in the metric and analytic properties of measures and domains.
Link:
Workshop: