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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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.

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

First available in Project Euclid: 27 February 2014

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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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