The exponential decay rate of the lower bound for the first eigenvalue of compact manifolds

Morris Kalka; Elizabeth Mann; Dagang Yang; Aleksey Zinger

doi:10.1142/S0129167X97000160

The exponential decay rate of the lower bound for the first eigenvalue of compact manifolds

Morris Kalka
, Elizabeth Mann
, Dagang Yang
, Aleksey Zinger

Mathematics

Tulane University
Harvard University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

This paper provides the optimal exponential decay rate of the lower bound for the first positive eigenvalue of the Laplacian operator on a compact Riemannian manifold with a negative lower bound on the Ricci curvature and with large diameter. For manifolds with boundary, suitable convexity conditions are assumed.

Original language	English
Pages (from-to)	345-355
Number of pages	11
Journal	International Journal of Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.1142/S0129167X97000160
State	Published - May 1997

Keywords

Eigenfunction
First eigenvalue
Geometric analysis
Gradient estimate
Ricci curvature
Riemannian manifold

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10.1142/S0129167X97000160

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title = "The exponential decay rate of the lower bound for the first eigenvalue of compact manifolds",

abstract = "This paper provides the optimal exponential decay rate of the lower bound for the first positive eigenvalue of the Laplacian operator on a compact Riemannian manifold with a negative lower bound on the Ricci curvature and with large diameter. For manifolds with boundary, suitable convexity conditions are assumed.",

keywords = "Eigenfunction, First eigenvalue, Geometric analysis, Gradient estimate, Ricci curvature, Riemannian manifold",

author = "Morris Kalka and Elizabeth Mann and Dagang Yang and Aleksey Zinger",

year = "1997",

month = may,

doi = "10.1142/S0129167X97000160",

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volume = "8",

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T1 - The exponential decay rate of the lower bound for the first eigenvalue of compact manifolds

AU - Kalka, Morris

AU - Mann, Elizabeth

AU - Yang, Dagang

AU - Zinger, Aleksey

PY - 1997/5

Y1 - 1997/5

N2 - This paper provides the optimal exponential decay rate of the lower bound for the first positive eigenvalue of the Laplacian operator on a compact Riemannian manifold with a negative lower bound on the Ricci curvature and with large diameter. For manifolds with boundary, suitable convexity conditions are assumed.

AB - This paper provides the optimal exponential decay rate of the lower bound for the first positive eigenvalue of the Laplacian operator on a compact Riemannian manifold with a negative lower bound on the Ricci curvature and with large diameter. For manifolds with boundary, suitable convexity conditions are assumed.

KW - Eigenfunction

KW - First eigenvalue

KW - Geometric analysis

KW - Gradient estimate

KW - Ricci curvature

KW - Riemannian manifold

UR - https://www.scopus.com/pages/publications/0031133961

U2 - 10.1142/S0129167X97000160

DO - 10.1142/S0129167X97000160

M3 - Article

AN - SCOPUS:0031133961

SN - 0129-167X

VL - 8

SP - 345

EP - 355

JO - International Journal of Mathematics

JF - International Journal of Mathematics

IS - 3

ER -

The exponential decay rate of the lower bound for the first eigenvalue of compact manifolds

Abstract

Keywords

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