Geodesic
Analogs of the P\'olya--Szeg\H{o} and Macai inequalities for the Euclidean moment of inertia of a convex domain
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 70-79.

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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
Mots-clés : convex domain. 
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     title = {Analogs of the {P\'olya--Szeg\H{o}} and {Macai} inequalities for the {Euclidean} moment of inertia of a convex domain},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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L. I. Gafiyatullina. Analogs of the P\'olya--Szeg\H{o} and Macai inequalities for the Euclidean moment of inertia of a convex domain. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 70-79. http://geodesic.mathdoc.fr/item/INTO_2020_176_a6/

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