where: Centro De Giorgi

who: Valentino Magnani (Universita' di Pisa)

title: An intrinsic notion of mass in the Heisenberg group

abstract: In this talk we present a class of differential forms that allows us to give a new notion of mass for currents in the Heisenberg group. We show that the sub-Riemannian perimeter of a set can be thought of as the intrinsic mass of its boundary. In the case of regular k-dimensional surfaces, we show that their intrinsic mass corresponds to the (k+1)-dimensional spherical Hausdorff measure with respect to the Carnot-Caratheodory distance. These facts confirm how this notion of mass fits the natural sub-Riemannian geometry of the Heisenberg group.