Integral Identities for the boundary of a convex body (2207.06923v1)

Published 14 Jul 2022 in math.MG and math.PR

Abstract: We present the multidimensional versions of the Pleijel and Ambartzumian--Pleijel identities. We also obtain the generalization of both the Blaschke--Petkantschin and Z\"ahle formulae considering the case when some points are chosen inside the convex body and some on the boundary. Moreover, a version of the Z\"ahle formula for the polytopes is derived.

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Authors (1)

Tatiana Moseeva

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