A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
Abstract
We prove the Ashbaugh--Benguria conjecture for bounded domains with smooth boundary in Rm. More precisely, among all smooth bounded domains of fixed volume, the ball minimizes the sum of the reciprocals of the first m nonzero Neumann eigenvalues. Equality is attained precisely by balls.
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