A lower bound for the least eigenvalue of Δ+V

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1990 Germany English Publisher:Springer Science and Business Media LLCJournal:Manuscripta Mathematica, volume 69, pages 255-259 (issn: 0025-2611, eissn: 1432-1785,

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Authors: Bérard, Pierre;

doi: 10.1007/bf02567923

A lower bound for the least eigenvalue of Δ+V

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Abstract

Let \(M^ n\) be a closed n dimensional Riemannian manifold, let \(\Delta\) be the scalar Laplacian, and let V: \(M\to {\mathbb{R}}\) be continuous. The author gives a sufficient condition for \(\Delta +V\) to be positive in terms of geometric assumptions on M; the author also gives an application to a Bochner type vanishing theorem.

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Germany

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Keywords

Bochner type vanishing theorem, 510.mathematics, least eigenvalue, Spectral problems; spectral geometry; scattering theory on manifolds, Laplacian, Article

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