Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

2015/10/25 by Hassannezhad, Asma, Kokarev, Gerasim, Polterovich, Iosif
#Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1510.07281

Abstract

We revisit classical eigenvalue inequalities due to Buser, Cheng, and Gromov on closed Riemannian manifolds, and prove the versions of these results for the Dirichlet and Neumann boundary value problems. Eigenvalue multiplicity bounds and related open problems are also discussed.

Related

• Some inequalities and asymptotic formulas for eigenvalues on Riemannian manifolds
• Estimates for Eigenvalues of the Dirichlet Laplacian on Riemannian Manifolds
• Eigenvalues estimate for the Neumann problem on bounded domains
• Lower Bounds of the First Closed and Neumann Eigenvalues of Compact Manifolds with Positive Ricci Curvature
• A note on Kuttler-Sigillito's inequalities