Steiner formula and Gauss curvature in the Heisenberg group

In this talk I will present some results concerning a localized Steiner-type formula for tubular neighborhoods in the Carnot-Carathéodory metric and a possible definition of horizontal Gauss curvature for smooth surfaces in the first Heisenberg group. The talk is based on a joint works with Z.M. Balogh, F. Ferrari, B. Franchi, J.T. Tyson and K. Wildrick.