Upper bounds on the first eigenvalue for a diffusion operator via Bakry-Émery Ricci curvature |
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Authors: | Jia-Yong Wu |
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Institution: | Department of Mathematics, East China Normal University, Shanghai 200241, China |
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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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Keywords: | Bakry-É mery Ricci curvature Diffusion operator Eigenvalue estimate |
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