✦ LIBER ✦

Lower bounds for the first eigenvalue of the -Laplacian on compact manifolds with positive Ricci curvature

✍ Scribed by HuiChun Zhang

Publisher: Elsevier Science
Year: 2007
Tongue: English
Weight: 203 KB
Volume: 67
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2006.06.031

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✦ Synopsis

We give some lower bounds for the first eigenvalue of the p-Laplace operator on compact Riemannian manifolds with positive (or non-negative) Ricci curvature in terms of diameter of the manifolds. For compact manifolds with boundary, we consider the Dirichlet eigenvalue with some proper geometric hypothesis.

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✍ Harold Donnelly 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 188 KB

Suppose that f is an eigenfunction of -D with eigenvalue l ] 0. It is proved that where n is the dimension of M and c 1 depends only upon a bound for the absolute value of the sectional curvature of M and a lower bound for the injectivity radius of M. It is then shown that if M admits an isometric