arXiv:2611.13018v1 Announce Type: new Abstract: In 1999, Ashbaugh formulated the conjecture that the ball maximizes the ratio of the first two clamped buckling eigenvalues among bounded domains in Euclidean space. We disprove this conjecture in every dimension $d\ge2$ by constructing smooth connected domains with finitely many interior holes. The key observation is that a zero-value constraint on a concentric sphere close to the boundary of a ball increases the first two eigenvalues by the same relative amount to first order, whereas their ratio increases strictly at second order. A quantitative surface penalty and logarithmic cutoffs transfer this strict inequality to smooth perforated domains. The construction gives explicit geometric parameters depending only on the dimension \(d\).
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