Eigenvalue lower bounds through a generalized inradius
Rupert L. Frank, Ari Laptev, Durvudkhan Suragan
公開日: 2025/9/23
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.