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Eigenvalue lower bounds through a generalized inradius (2509.18878v1)
Published 23 Sep 2025 in math.SP, math.AP, and math.FA
Abstract: Lieb has shown a lower bound on the smallest Dirichlet eigenvalue of the Laplace operator in terms of a generalized inradius. We derive similar bounds for Robin eigenvalues, for eigenvalues of the polyharmonic operator and the sub-Laplacian on the Heisenberg group. We propose a method based on Hardy inequalities that is different from Lieb's approach.
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