Moscow Mathematical Journal
Volume 22, Issue 3, July–September 2022 pp. 377–392.
Crofton Formulae for Products
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.
Authors:
Dmitri Akhiezer (1) and Boris Kazarnovskii (1)
Author institution:(1) Institute for Information Transmission Problems, 19 B. Karetny per., 127051, Moscow, Russia
Summary:
Keywords: Crofton data, normal density, mixed volume.
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