Proves that the ball minimizes the sum of reciprocals of the first m nonzero Neumann eigenvalues among smooth bounded domains of fixed volume in R^m, with equality only for balls.
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Proves that for bounded domains in R^N (N≥2), the sum from i=1 to N of λ1/(λ_{i+1}-λ1) is at least N/(j_{N/2,1}^2/j_{N/2-1,1}^2 -1), with equality precisely when the domain is a ball up to H^1-capacity zero.
citing papers explorer
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A proof of the Ashbaugh--Benguria conjecture for reciprocal sums of Neumann eigenvalues
Proves that the ball minimizes the sum of reciprocals of the first m nonzero Neumann eigenvalues among smooth bounded domains of fixed volume in R^m, with equality only for balls.
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The Ashbaugh--Benguria reciprocal-gap conjecture for Dirichlet eigenvalues
Proves that for bounded domains in R^N (N≥2), the sum from i=1 to N of λ1/(λ_{i+1}-λ1) is at least N/(j_{N/2,1}^2/j_{N/2-1,1}^2 -1), with equality precisely when the domain is a ball up to H^1-capacity zero.