Illinois Journal of Mathematics

An exact solution to an equation and the first eigenvalue of a compact manifold

Jun Ling

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Abstract

We study an exact solution to a singular ordinary differential equation and use the solution to give a new estimate on the lower bound of the first non-zero eigenvalue of a closed Riemannian manifold with a negative lower bound on the Ricci curvature in terms of the lower bound on the Ricci curvature and the largest interior radius of the nodal domains of the eigenfunction. This provides a new way to estimate eigenvalues.

Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 853-860.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131106

Digital Object Identifier
doi:10.1215/ijm/1258131106

Mathematical Reviews number (MathSciNet)
MR2379726

Zentralblatt MATH identifier
1147.58032

Subjects
Primary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]

Citation

Ling, Jun. An exact solution to an equation and the first eigenvalue of a compact manifold. Illinois J. Math. 51 (2007), no. 3, 853--860. doi:10.1215/ijm/1258131106. https://projecteuclid.org/euclid.ijm/1258131106


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