Calculus of Variations and Geometric Measure Theory

An intrinsic notion of mass in the Heisenberg group

Valentino Magnani (Dip. Mat. Univ. Pisa)

created by alberti on 06 May 2004

27 may 2004


Seminari di Calcolo delle Variazioni

when: Giovedi' 27 maggio, ore 16 Thursday, May 27, 4 pm

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.

posted by Giovanni Alberti