Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II

Details Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II

2010-10-20

arxiv.org/abs/1010.4175v4

Mathematics

Differential Geometry

13 pages. Remarks 1.2, 1.3,1.4, 2.2, 2.3 and 2.4 added or improved; Section 3 in old version deleted. References 21,26 and 30

Scientific paper

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).

Affiliated with

Also associated with

No associations

Rating

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature II will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717228