Bounds for Eigenfunctions of the Laplacian on Compact Riemannian Manifolds

✍ Scribed by Harold Donnelly

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 188 KB
• Volume: 187
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2001.3817

✦ Synopsis

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 circle action, and the metric is generic, one has exceptional sequences of eigenfunctions satisfying the complementary bounds ||f k || . \ c 2 l n-1 8 k ||f|| 2 .