Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

Asma Hassannezhad; Gerasim Kokarev; Iosif Polterovich

doi:10.4171/JST/143

Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

Asma Hassannezhad, Gerasim Kokarev, Iosif Polterovich

School of Mathematics

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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 language	English
Pages (from-to)	807-835
Number of pages	28
Journal	Journal of Spectral Theory
Volume	6
Issue number	4
Early online date	9 Dec 2016
DOIs	https://doi.org/10.4171/JST/143
Publication status	Published - 2016

Keywords

Laplace operator
Riemannian manifold
eigenvalue inequalities
counting function

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title = "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.",

keywords = "Laplace operator, Riemannian manifold, eigenvalue inequalities, counting function",

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AU - Hassannezhad, Asma

AU - Kokarev, Gerasim

AU - Polterovich, Iosif

PY - 2016

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N2 - 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.

AB - 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.

KW - Laplace operator

KW - Riemannian manifold

KW - eigenvalue inequalities

KW - counting function

U2 - 10.4171/JST/143

DO - 10.4171/JST/143

M3 - Article (Academic Journal)

SN - 1664-039X

VL - 6

SP - 807

EP - 835

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

IS - 4

ER -

Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

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