Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications
Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications
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DOI：
10.1016/j.geomphys.2023.104997
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发表时间：
2023-06
影响因子：
1.5
通讯作者：
Xin Song;Ling Wu;Meng Zhu
中科院分区：
文献类型：
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作者：
Xin Song;Ling Wu;Meng Zhu
我们建立了完全黎曼流形上Laplace-Beltrami算子热核的高斯上界，其中Bakry-Émery Ricci曲率有界以下。作为应用，我们首先证明了Bakry-Émery Ricci曲率张量的势函数至多为二次增长时非负次调和函数的L - liouville性质。然后导出了闭流形上拉普拉斯-贝尔特拉米算子特征值的下界。得到了底谱的上界。
We establish a Gaussian upper bound of the heat kernel for the Laplace-Beltrami operator on complete Riemannian manifolds with Bakry-Émery Ricci curvature bounded below. As applications, we first prove an L 1-Liouville property for non-negative subharmonic functions when the potential function of the Bakry-Émery Ricci curvature tensor is of at most quadratic growth. Then we derive lower bounds of the eigenvalues of the Laplace-Beltrami operator on closed manifolds. An upper bound of the bottom spectrum is also obtained.