Valuations with Crofton formula and Finsler geometry
- Bernig, Andreas Département de Mathématiques, Université de Fribourg, Switzerland
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28.08.2006
Published in:
- Advances in Mathematics. - 2007, vol. 210, no. 2, p. 733-753
English
Valuations admitting a smooth Crofton formula are studied using Geometric Measure Theory and Rumin's cohomology of contact manifolds. The main technical result is a current representation of a valuation with a smooth Crofton formula. A geometric interpretation of Alesker's product is given for such valuations. As a first application in Finsler geometry, a short proof of the theorem of Gelfand–Smirnov that Crofton densities are projective is derived. The Holmes–Thompson volumes in a projective Finsler space are studied. It is shown that they induce in a natural way valuations and that the Alesker product of the k-dimensional and the l-dimensional Holmes–Thompson valuation is the (k+l)-dimensional Holmes–Thompson valuation.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
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- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 8427
- DOI 10.1016/j.aim.2006.07.009
- Persistent URL
- https://folia.unifr.ch/unifr/documents/300581
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