Lower bounds for the sum of the reciprocals of eigenvalues of bounded domains in $\mathbb{R}^{n}$, spheres, and closed orientable surfaces
Abstract
We establish lower bounds for sums of reciprocals of Laplacian eigenvalues for bounded Euclidean domains, spheres and surfaces. For bounded Euclidean domains, we recover a sharp inequality that extends Bucur and Henrot’s upper bound on the second Neumann eigenvalue. For spheres and surfaces, we obtain new Li- and Yau-type bounds and we discuss them in terms of conformal volume.
Fields of Study & Subjects
Advanced Mathematical Modeling in Engineering
Nonlinear Partial Differential Equations
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Journal of Spectral Theory
- Publication date
- 1 September 2026
- Language
- EN