Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

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.

19 pages, final version; to appear in the Yuri Safarov memorial volume of the Journal of Spectral Theory

References in corpus (2)

• Eigenvalue multiplicity and volume growth
• On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces