Abstract and Applied Analysis

A Global Curvature Pinching Result of the First Eigenvalue of the Laplacian on Riemannian Manifolds

Peihe Wang and Ying Li

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Abstract

The paper starts with a discussion involving the Sobolev constant on geodesic balls and then follows with a derivation of a lower bound for the first eigenvalue of the Laplacian on manifolds with small negative curvature. The derivation involves Moser iteration.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 237418, 5 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511812

Digital Object Identifier
doi:10.1155/2013/237418

Mathematical Reviews number (MathSciNet)
MR3039135

Zentralblatt MATH identifier
1275.53040

Citation

Wang, Peihe; Li, Ying. A Global Curvature Pinching Result of the First Eigenvalue of the Laplacian on Riemannian Manifolds. Abstr. Appl. Anal. 2013 (2013), Article ID 237418, 5 pages. doi:10.1155/2013/237418. https://projecteuclid.org/euclid.aaa/1393511812


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References

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