Integral Identities for the boundary of a convex body
Metric Geometry
2022-07-15 v1 Probability
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.
Keywords
Cite
@article{arxiv.2207.06923,
title = {Integral Identities for the boundary of a convex body},
author = {Tatiana Moseeva},
journal= {arXiv preprint arXiv:2207.06923},
year = {2022}
}
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12 pages