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
A probabilistic approach to the first Dirichlet eigenvalue on non-compact Riemannian manifold
β Scribed by Wang Fengyu
- Book ID
- 110556377
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 1997
- Tongue
- English
- Weight
- 433 KB
- Volume
- 13
- Category
- Article
- ISSN
- 1439-7617
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π SIMILAR VOLUMES
## Abstract We give a new estimate on the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature and provide a solution for a conjecture of H. C. Yang. (Β© 2007 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
An estimate for the first eigenvalue of the Dirac operator on compact Riemannian spin manifold of positive scalar curvature admitting a parallel one-form is found. The possible universal covering spaces of the manifolds on which the smallest possible eigenvalue is attained are also listed. Moreover,