Kinematic formulas for tensor valuations
Differential Geometry
2018-07-09 v2 Metric Geometry
Abstract
We prove new kinematic formulas for tensor valuations and simplify previously known Crofton formulas by using the recently developed algebraic theory of translation invariant valuations. The heart of the paper is the computation of the Alesker-Fourier transform on the large class of spherical valuations, which is achieved by differential-geometric and representation theoretical tools. We also describe in explicit form the product and convolution of tensor valuations.
Cite
@article{arxiv.1402.2750,
title = {Kinematic formulas for tensor valuations},
author = {Andreas Bernig and Daniel Hug},
journal= {arXiv preprint arXiv:1402.2750},
year = {2018}
}
Comments
48 pages; minor changes