### 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 Zoltàn Balogh, Fausto Ferrari, Bruno Franchi and Kevin Wildrick

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DOI: 10.6092/issn.2240-2829/6693

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