English

Principal Kinematic Formulas for Germs of Closed Definable Sets

Algebraic Geometry 2021-01-01 v1 Differential Geometry

Abstract

We prove two principal kinematic formulas for germs of closed definable sets in Rn\mathbb{R}^n, that generalize the Cauchy-Crofton formula for the density due to Comte and the infinitesimal linear kinematic formula due to the author. In this setting, we do not integrate on the space of euclidian motions, but on the manifold SO(n)×Sn1SO(n) \times S^{n-1}.

Keywords

Cite

@article{arxiv.2012.14783,
  title  = {Principal Kinematic Formulas for Germs of Closed Definable Sets},
  author = {Nicolas Dutertre},
  journal= {arXiv preprint arXiv:2012.14783},
  year   = {2021}
}