JournalsjstVol. 6, No. 4pp. 807–835

Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

  • Asma Hassannezhad

    Bonn, Germany

  • Gerasim Kokarev

    Ludwig-Maximilians-Universität München, Germany

  • Iosif Polterovich

    Université de Montréal, Canada
Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound cover
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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.

Cite this article

Asma Hassannezhad, Gerasim Kokarev, Iosif Polterovich, Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound. J. Spectr. Theory 6 (2016), no. 4, pp. 807–835

DOI 10.4171/JST/143