2 2 Ju n 20 04 The First Dirichlet Eigenvalue and the Li Conjecture ∗
نویسنده
چکیده
We give a new estimate on the lower bound for the first Dirichlet eigenvalue for the compact manifolds with boundary and positive Ricci curvature in terms of the diameter and the lower bound of the Ricci curvature and give an affirmative answer to the conjecture of P. Li for the Dirichlet eigenvalue.
منابع مشابه
Ju n 20 04 The First Closed Eigenvalue and the Li Conjecture ∗
We give new estimate on the lower bound for the first non-zero eigenvalue for the closed manifolds with positive Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of P. Li for the closed eigenvalue.
متن کاملun 2 00 4 The First Dirichlet Eigenvalue and Li ’ s Conjecture ∗
We give a new estimate on the lower bound for the first Dirichlet eigenvalue for the compact manifolds with boundary and positive Ricci curvature in terms of the diameter and the lower bound of the Ricci curvature and give an affirmative answer to the conjecture of P. Li for the Dirichlet eigenvalue.
متن کاملul 2 00 4 The First Dirichlet Eigenvalue and the Li Conjecture ∗
We give a new estimate on the lower bound for the first Dirichlet eigenvalue for the compact manifolds with boundary and positive Ricci curvature in terms of the diameter and the lower bound of the Ricci curvature and give an affirmative answer to the conjecture of P. Li for the Dirichlet eigenvalue.
متن کاملul 2 00 4 The First Dirichlet Eigenvalue and the Yang Conjecture ∗
We estimate the lower bound of the first Dirichlet eigenvalue of a compact Riemannian manifold with negative lower bound of Ricci curvature in terms of the diameter and the lower bound of Ricci curvature and give an affirmative answer to the conjecture of H. C. Yang for the first Dirichlet eigenvalue.
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Let Ω be some domain in the hyperbolic space Hn (with n ≥ 2) and S1 the geodesic ball that has the same first Dirichlet eigenvalue as Ω. We prove the Payne-Pólya-Weinberger conjecture for Hn, i.e., that the second Dirichlet eigenvalue on Ω is smaller or equal than the second Dirichlet eigenvalue on S1. We also prove that the ratio of the first two eigenvalues on geodesic balls is a decreasing f...
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