Geodesic
Inequalities for the Eigenvalues of the Riesz Potential
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 844-850

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It is proved that, of all the domains with identical measure, it is the ball that maximizes the first eigenvalue of the Riesz potential. It is shown that the sum of the squares of all the eigenvalues is also maximized in the ball among all the domains with identical measure.
Keywords: eigenvalue, spectral geometry, Riesz potential. 
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     author = {T. Sh. Kal'menov and D. Suragan},
     title = {Inequalities for the {Eigenvalues} of the {Riesz} {Potential}},
     journal = {Matemati\v{c}eskie zametki},
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T. Sh. Kal'menov; D. Suragan. Inequalities for the Eigenvalues of the Riesz Potential. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 844-850. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a4/