Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

Hassannezhad, Asma; Kokarev, Gerasim; Polterovich, Iosif (2016): Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound. In: Journal of Spectral Theory, Vol. 6, No. 4: pp. 807-835

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.

• Item Type: Journal article
• Form of publication: Publisher's Version
• Keywords: Laplace operator; Riemannian manifold; eigenvalue inequalities; counting function
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1664-039X
• Alliance/National Licence: This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
• Language: English