Principal Kinematic Formulas for Germs of Closed Definable Sets

preprint2020arXivOpen access

We prove two principal kinematic formulas for germs of closed definable sets in $\mathbb{R}^n$ , 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 $SO(n) \times S^{n-1}$ .

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Principal Kinematic Formulas for Germs of Closed Definable Sets

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