Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4619491 | Journal of Mathematical Analysis and Applications | 2010 | 9 Pages |
Abstract
Let L=Δ−∇φ⋅∇ be a symmetric diffusion operator with an invariant measure on a complete Riemannian manifold. In this paper we give an upper bound estimate on the first eigenvalue of the diffusion operator L on the complete manifold with the m-dimensional Bakry–Émery Ricci curvature satisfying Ricm,n(L)⩾−(n−1), and therefore generalize a Cheng's result on the Laplacian (S.-Y. Cheng (1975) [8]) to the case of the diffusion operator.
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