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Counterexamples to a higher-index Dirichlet eigenvalue-ratio conjecture
Let $λ_k(Ω)$ denote the $k$th Dirichlet Laplacian eigenvalue of a bounded planar domain $Ω$, with eigenvalues counted with multiplicity. We disprove a conjectured higher-index extension of the Payne--Pólya--Weinberger inequality that was recorded as an open problem by Ashbaugh. For every integer $m\
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