Lower bounds for the sum of the reciprocals of eigenvalues of bounded domains in $\mathbb{R}^{n}$, spheres, and closed orientable surfaces
Year: 2026
Type: article
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.
Source: Journal of Spectral Theory
DOI: 10.4171/jst/627
Author: Mehdi Eddaoudi
Institution: Université Laval
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4407760084