STEINER FORMULA AND GAUSSIAN CURVATURE IN THE HEISENBERG GROUP

The classical Steiner formula expresses the volume of the epsilon-neighborhood Omega(epsilon) of a bounded and regular domain Omega subset of R-n as a polynomial of degree n in epsilon. In particular, the coefficients of this polynomial are the integrals of functions of the curvatures of the boundary partial derivative Omega. The aim of this note is to present the Heisenberg counterpart of this result. The original motivation for studying this kind of extension is to try to identify a suitable candidate for the notion of horizontal Gaussian curvature.The results presented in this note are contained in the paper [4] written in collaboration with Zoltan Balogh, Fausto Ferrari, Bruno Franchi and Kevin Wildrick.