论文标题
对贝克里（Bakry）歧管的特征值估算
Eigenvalue Estimates on Bakry-Emery Manifolds
论文作者
论文摘要
我们证明了有或没有边界的紧凑型巴克里河畔歧管的特征值的下限。第一个特征值的下限依赖于广义的最大原理，该原理允许将riemannian设置中的梯度估计直接应用于贝克里（Bakry）的设置。使用热内核估计值和合适的Sobolev不等式证明了所有特征值的下限。
We demonstrate lower bounds for the eigenvalues of compact Bakry-Emery manifolds with and without boundary. The lower bounds for the first eigenvalue rely on a generalised maximum principle which allows gradient estimates in the Riemannian setting to be directly applied to the Bakry-Emery setting. Lower bounds for all eigenvalues are demonstrated using heat kernel estimates and a suitable Sobolev inequality.
