Abstract and Applied Analysis
Volume 2013 (2013), Article ID 237418, 5 pages
http://dx.doi.org/10.1155/2013/237418
Research Article

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

Peihe Wang1 and Ying Li2

1School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu 273165, China
2College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 8 December 2012; Revised 19 February 2013; Accepted 9 March 2013

Academic Editor: Wenming Zou

Copyright © 2013 Peihe Wang and Ying Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.