New inequalities for eigenvalues of the Dirichlet Laplacian on the hyperbolic space
Analysis of PDEs
2026-04-23 v1 Differential Geometry
Abstract
In this paper, motivated by study on universal inequalities for eigenvalues of the Dirichlet Laplacian, we prove some new inequalities for eigenvalues of the Dirichlet Laplacian on the hyperbolic space. In particular, we verify Cheng's conjecture (Adv. Lect. Math. 37, 2017) up to loss of for two special kinds of bounded domains in the hyperbolic space.
Keywords
Cite
@article{arxiv.2604.20343,
title = {New inequalities for eigenvalues of the Dirichlet Laplacian on the hyperbolic space},
author = {Yong Luo},
journal= {arXiv preprint arXiv:2604.20343},
year = {2026}
}
Comments
10 pages