Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2020, Volume 176, Pages 70–79
DOI: https://doi.org/10.36535/0233-6723-2020-176-70-79 (Mi into588) 		 
Analogs of the Pólya–Szegő and Macai inequalities for the Euclidean moment of inertia of a convex domain

L. I. Gafiyatullina

Kazan (Volga Region) Federal University
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DOI: https://doi.org/10.36535/0233-6723-2020-176-70-79
Abstract: In this paper, we obtain two-sided estimates for the Euclidean moment of inertia $\mathrm{I}_{2}(G) $ of a convex domain $G$ on the plane in terms of geometric characteristics of this domain similar to the Pólya–Szegő and Makai inequalities for the torsional rigidity.
Keywords: torsional rigidity, Euclidean moment of a domian relative to the boundary, isoperimetric inequality, distance function, boundary of a domain, convex domain.
Document Type: Article
UDC: 514.8
MSC: 51K05
Language: Russian
Citation: L. I. Gafiyatullina, “Analogs of the Pólya–Szegő and Macai inequalities for the Euclidean moment of inertia of a convex domain”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176, VINITI, Moscow, 2020, 70–79
Citation in format AMSBIB
\Bibitem{Gaf20}
\by L.~I.~Gafiyatullina
\paper Analogs of the P\'olya--Szeg\H{o} and Macai inequalities for the Euclidean moment of inertia of a convex domain
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 176
\pages 70--79
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into588}
\crossref{https://doi.org/10.36535/0233-6723-2020-176-70-79}
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