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
Linear approximation of the first eigenvalue on compact manifolds
β Scribed by Mufa Chen; E. Scacciatelli; Liang Yao
- Publisher
- SP Science China Press
- Year
- 2002
- Tongue
- English
- Weight
- 224 KB
- Volume
- 45
- Category
- Article
- ISSN
- 1674-7283
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## 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)
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 hyp