The spectrum of the Laplacian on the warped products of Riemannian manifolds
β Scribed by N. V. Glotko
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 2008
- Tongue
- English
- Weight
- 243 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0037-4466
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The purpose of the present paper is to study the following problem. Given a warped product M := B x s F, OF = q~, give conditions that B and f must satisfy for the existence of the Riemannian simple double of M.
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
The ΓΏrst nonlinear eigenvalue of the p-Laplacian (p ΒΏ 2) is investigated for a compact manifold of nonnegative Ricci curvature with or without boundary. Lower bound estimates are given by the diameter or the inscribed radius. The key ingredients in proofs are the formula of Bochner-Weitz onbeck type