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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 510, Pages 172–188 (Mi znsl7200)  
Integral identities for the boundary of a convex body

T. D. Moseeva

Euler International Mathematical Institute, St. Petersburg
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Abstract: We present the multidimensional versions of the Pleijel and Ambartzumian–Pleijel identities. We also obtain the generalization of both the Blaschke–Petkantschin and Zähle formulae considering the case when some points are chosen inside the convex body and some on the boundary. Moreover, a version of the Zähle formula for the polytopes is derived.
Key words and phrases: Blaschke–Petkantschin formula, Zähle formula, Pleijel identity, Ambartzumian-Pleijel identity, random chord.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-287
Foundation for the Development of Theoretical Physics and Mathematics BASIS
Received: 31.08.2022
Bibliographic databases:
Document Type: Article
UDC: 519.2
Language: Russian
Citation: T. D. Moseeva, “Integral identities for the boundary of a convex body”, Probability and statistics. Part 32, Zap. Nauchn. Sem. POMI, 510, POMI, St. Petersburg, 2022, 172–188
Citation in format AMSBIB
\Bibitem{Mos22}
\by T.~D.~Moseeva
\paper Integral identities for the boundary of a convex body
\inbook Probability and statistics. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2022
\vol 510
\pages 172--188
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7200}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4503195}
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