A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues

Abstract

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 balls.

arXiv comment10 pages. Accepted for publication in Geometric and Functional Analysis. This version incorporates revisions made during peer review