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Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)807-835
Number of pages28
JournalJournal of Spectral Theory
Volume6
Issue number4
Early online date9 Dec 2016
DOIs
DateAccepted/In press - 1 Dec 2016
DateE-pub ahead of print - 9 Dec 2016
DatePublished (current) - 2016

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.

    Research areas

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

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via European Mathematical Society at https://doi.org/10.4171/JST/143 . Please refer to any applicable terms of use of the publisher.

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