Geodesic
Some weak geometric inequalities for the Riesz potential
Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 42-50

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In the present paper, we prove that the first eigenvalue of the Riesz potential is weakly maximised in a quasi-ball among all Haar measurable sets on homogeneous Lie groups. It is an analogue of the classical Rayleigh–Faber–Krahn inequality for the Riesz potential. We also prove a weak version of the Hong–Krahn–Szegö inequality for the Riesz potential on homogeneous Lie groups. 
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     author = {A. Kassymov},
     title = {Some weak geometric inequalities for the {Riesz} potential},
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     url = {http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a3/}
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A. Kassymov. Some weak geometric inequalities for the Riesz potential. Eurasian mathematical journal, Tome 11 (2020) no. 3, pp. 42-50. http://geodesic.mathdoc.fr/item/EMJ_2020_11_3_a3/