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A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
We prove the Ashbaugh--Benguria conjecture for bounded domains with Lipschitz boundary in $\mathbb R^m$. More precisely, among all bounded Lipschitz domains of fixed volume, the ball minimizes the sum of the reciprocals of the first $m$ nonzero Neumann eigenvalues. Equality is attained precisely by
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