Eigenvalue lower bounds through a generalized inradius

Published 23 Sep 2025 in math.SP, math.AP, and math.FA | (2509.18878v1)

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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Eigenvalue lower bounds through a generalized inradius (5 likes, 0 questions)