Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

Asma Hassannezhad, Gerasim Kokarev, Iosif Polterovich

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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.
Original languageEnglish
Pages (from-to)807-835
Number of pages28
JournalJournal of Spectral Theory
Volume6
Issue number4
Early online date9 Dec 2016
DOIs
Publication statusPublished - 2016

Keywords

  • Laplace operator
  • Riemannian manifold
  • eigenvalue inequalities
  • counting function

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