Eigenvalue lower bounds through a generalized inradius
Spectral Theory
2025-09-24 v1 Analysis of PDEs
Functional Analysis
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.
Cite
@article{arxiv.2509.18878,
title = {Eigenvalue lower bounds through a generalized inradius},
author = {Rupert L. Frank and Ari Laptev and Durvudkhan Suragan},
journal= {arXiv preprint arXiv:2509.18878},
year = {2025}
}
Comments
16 pages