Steiner Formula and Gaussian Curvature in the Heisenberg Group


  • Eugenio Vecchi University of Bologna



Heisenberg group, Steiner's formula


The classical Steiner formula expresses the volume of the ∈-neighborhood Ωof a bounded and regular domain  Ω⊂Rn 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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How to Cite

Vecchi, E. (2017). Steiner Formula and Gaussian Curvature in the Heisenberg Group. Bruno Pini Mathematical Analysis Seminar, 7(1), 97–115.