Moscow Mathematical Journal

Volume 22, Issue 3, July–September 2022 pp. 377–392.

Crofton Formulae for Products

Authors: Dmitri Akhiezer (1) and Boris Kazarnovskii (1)
Author institution:(1) Institute for Information Transmission Problems, 19 B. Karetny per., 127051, Moscow, Russia

Summary:

Abstract. We suggest an algorithm allowing to get some new integral-geometric formulae from the existing formulae of Crofton type. In particular, for classical Crofton formulae in which the answer depends on the Riemannian volume, we obtain generalizations in terms of the mixed Riemannian volume defined in the paper. The algorithm is based on the calculations in the ring of normal densities constructed in the previous work of the authors.

2020 Math. Subj. Class. 52A39, 58A05.

Keywords: Crofton data, normal density, mixed volume.

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