Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-Émery Ricci Curvature Condition

@article{Wu2021EigenvalueEF,
  title={Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-{\'E}mery Ricci Curvature Condition},
  author={Ling Wu and Xin Song and Meng Zhu},
  journal={Potential Analysis},
  year={2021}
}
On closed Riemannian manifolds with Bakry-Émery 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 drifted Laplacian. The lower bound of the kth eigenvalue depends on k, Bakry-Émery Ricci curvature lower bound, 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… 
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