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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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 |
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doaj-8ee9841b597341639f6e2d9f68c3d7c22020-11-24T22:39:11ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292016-12-01719711510.6092/issn.2240-2829/66936090Steiner Formula and Gaussian Curvature in the Heisenberg GroupEugenio Vecchi0University of BolognaThe 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 Wildrickhttps://mathematicalanalysis.unibo.it/article/view/6693Heisenberg groupSteiner's formula |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Eugenio Vecchi |
| spellingShingle |
Eugenio Vecchi Steiner Formula and Gaussian Curvature in the Heisenberg Group Bruno Pini Mathematical Analysis Seminar Heisenberg group Steiner's formula |
| author_facet |
Eugenio Vecchi |
| author_sort |
Eugenio Vecchi |
| title |
Steiner Formula and Gaussian Curvature in the Heisenberg Group |
| title_short |
Steiner Formula and Gaussian Curvature in the Heisenberg Group |
| title_full |
Steiner Formula and Gaussian Curvature in the Heisenberg Group |
| title_fullStr |
Steiner Formula and Gaussian Curvature in the Heisenberg Group |
| title_full_unstemmed |
Steiner Formula and Gaussian Curvature in the Heisenberg Group |
| title_sort |
steiner formula and gaussian curvature in the heisenberg group |
| publisher |
University of Bologna |
| series |
Bruno Pini Mathematical Analysis Seminar |
| issn |
2240-2829 |
| publishDate |
2016-12-01 |
| description |
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 |
| topic |
Heisenberg group Steiner's formula |
| url |
https://mathematicalanalysis.unibo.it/article/view/6693 |
| work_keys_str_mv |
AT eugeniovecchi steinerformulaandgaussiancurvatureintheheisenberggroup |
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