Steiner Formula and Gaussian Curvature in the Heisenberg Group
The classical Steiner formula expresses the volume of the ∈-neighborhood Ω∈ of 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 prese...
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| Format: | Article |
| Language: | English |
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University of Bologna
2016-12-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/6693 |
| Summary: | The classical Steiner formula expresses the volume of the ∈-neighborhood Ω∈ of 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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| ISSN: | 2240-2829 |