Steiner Formula and Gaussian Curvature in the Heisenberg Group

Abstract

The classical Steiner formula expresses the volume of the ∈-neighborhood Ω ∈ of a bounded and regular domain  Ω⊂R n as a polynomial of degree n in ∈. In particular, the coefficients of this polynomial are the integrals of functions of the curvatures of the boundary ∂Ω. 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