Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-Émery Ricci Curvature Condition
Eigenvalue Estimates for Beltrami-Laplacian Under Bakry-Émery Ricci Curvature Condition
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DOI：
10.1007/s11118-022-10062-5
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发表时间：
2021-08
影响因子：
1.1
通讯作者：
Ling Wu;Xin Song;Meng Zhu
中科院分区：
文献类型：
--
作者：
Ling Wu;Xin Song;Meng Zhu
在具有Bakry-Émery Ricci曲率和势函数梯度有界的闭黎曼流形上，我们得到了Beltrami-Laplacian而不是加权Laplacian的所有正特征值的下界。第k个特征值的下界依赖于k、Bakry-Émery Ricci曲率的下界、势函数的梯度界以及流形的维数和直径的上界，但不涉及流形的体积.
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 weighted Laplacian. The lower bound of thekth eigenvalue depends onk, the lower bound of Bakry-Émery 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.