Lipschitz hypersurfaces and perimeter in Carnot-Carathéodory spaces Abstract

Davide Vittone

(Dip. Matematica, Univ. di Padova)

Event: ERC Workshop on Geometric Analysis on sub-Riemannian and Metric Spaces

Date: Oct 14, 2011, time: 11:40

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. The notion of "intrinsic Lipschitz" hypersurface has been recently introduced in Carnot groups by B. Franchi, R. Serapioni and F. Serra Cassano. We will discuss an equivalent definition which can be stated in the more general framework of Carnot-Carathéodory spaces and prove that intrinsic Lipschitz domains have locally finite perimeter.
Properties of the perimeter measure (e.g., an area-type formula, Ahlfors regularity) will be discussed. If time permits, we will also show some application to trace problems for functions with Bounded Variation in Carnot-Carathéodory spaces.