Geodesic
Isoperimetric monotony of the Lp-norm of the warping function of a~plane simply connected domain
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 59-68.

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Let G be a simply connected domain and let u(x,G) be its warping function. We prove that Lp-norms of functions u and u−1 are monotone with respect to the parameter p. This monotony also gives isoperimetric inequalities for norms that correspond to different values of the parameter p. The main result of this paper is a generalization of classical isoperimetric inequalities of St. Venant–Pólya and the Payne inequalities.
Mots-clés : torsional rigidity, isoperimetric inequalities, isoperimetric monotony, Schwarz symmetrization, Kohler-Jobin symmetrization. 
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R. G. Salakhudinov. Isoperimetric monotony of the $L^p$-norm of the warping function of a~plane simply connected domain. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2010), pp. 59-68. https://geodesic-test.mathdoc.fr/item/IVM_2010_8_a6/

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