科研之友
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摘要
On closed Riemannian manifolds with Bakry-emery Ricci curvature bounded from below and bounded gradient of the potential function, we obtain lower bounds for all positive eigenvalues of the Beltrami-Laplacian instead of the weighted Laplacian. The lower bound of the k th eigenvalue depends on k, the lower bound of Bakry-emery Ricci curvature, the gradient bound of the potential function, and the dimension and diameter upper bound of the manifold, but the volume of the manifold is not involved.
