Faculté des sciences

## Valuations with Crofton formula and Finsler geometry

### In: Advances in Mathematics, 2007, vol. 210, no. 2, p. 733-753

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... More