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- Jun LING
- 2008

We give new estimates on the lower bounds for the first closed and Neumann eigenvalues for the compact manifolds with positive Ricci curvature in terms of the diameter and the lower bound of Ricci curvature.

- Jun LING
- 1997

We give a lower bound for the first gap λ2 − λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in a class of Riemannian manifolds, namely λ2 − λ1 ≥ π diameter(Ω) + ( 12 π − 1)α. For the Laplacian on disks in Rn, we have λ2 − λ1 ≥ 4 3 π diameter(Ω) .

- Jun LING
- 2008

We give an estimate on the lower bound of the first non-zero eigenvalue of the Laplacian for a closed Riemannian manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature.

- Jun LING
- 2004

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.

- Jun LING
- 2004

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.

- JUN LING
- 2008

The study of behavior of the eigenvalues of differential operators along the flow of metrics is very active. We list a few such studies as follows. Perelman [9] proved the monotonicity of the first eigenvalue of the operator −∆ + 1 4 R along the Ricci flow by using his entropy and was then able to rule out nontrivial steady or expanding breathers on compact… (More)

- Jun LING
- 2008

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.

- Jun LING
- 2008

We give a new estimate on the lower bound for the first Dirichlet eigenvalue for a compact manifold with positive Ricci curvature in terms of the in-diameter and the lower bound of the Ricci curvature. The result improves the previous estimates.

- JUN LING
- 2008

We construct a class of monotonic quantities along the normalized Ricci flow on closed n-dimensional manifolds.

- Jun LING
- 2004

We give a new lower bound for the first gap λ2−λ1 of the Dirichlet eigenvalues of the Schrödinger operator on a bounded convex domain Ω in Rn or Sn and greatly sharpens the previous estimates. The new bound is explicit and computable.