New inequalities for eigenvalues of the Dirichlet Laplacian on the hyperbolic space

Published: April 22, 2026PDF arXiv

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 $ε$ for two special kinds of bounded domains in the hyperbolic space.