Vectorial analogues of Cauchy’s surface area formula
Hug, Daniel
1; Schneider, Rolf
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)
1; Schneider, Rolf1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)
Abstract:
Cauchy's surface area formula says that for a convex body K in n-dimensional Euclidean space the mean value of the $(n−1)$-dimensional volumes of the orthogonal projections of K to hyperplanes is a constant multiple of the surface area of K. We prove an analogous formula, with the volumes of the projections replaced by their moment vectors. This requires to introduce a new vector-valued valuation on convex bodies.
| Zugehörige Institution(en) am KIT | Institut für Stochastik (STOCH) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2023 |
| Sprache | Englisch |
| Identifikator | KITopen-ID: 1000168202 |
| Umfang | 10 S. |
| Vorab online veröffentlicht am | 23.07.2023 |
| Schlagwörter | Cauchy’s surface area formula, moment vector, tensor-valued valuation |
| Nachgewiesen in | Dimensions arXiv |
| Relationen in KITopen |