4 papers
A direct approach to sharp Li-Yau Estimates on closed manifolds with negative Ricci lower bound
Xingyu Song, Ling Wu, Meng Zhu
Recently, Qi S.Zhang [26] has derived a sharp Li-Yau estimate for positive solutions of the heat equation on closed Riemannian manifolds with the Ricci curvature bounded below by a…
Heat kernel estimate for the Laplace-Beltrami operator under Bakry-Émery Ricci curvature condition and applications
Xingyu Song, Ling Wu, Meng Zhu
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 applica…
Li-Yau gradient estimates on closed manifolds under bakry-emery ricci curvature conditions
Xingyu Song, Ling Wu
In this paper, motivated by the work of Qi S. Zhang in [28], we derive Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Emery Ric…
Eigenvalue estimates for Beltrami-Laplacian under Bakry-Émery Ricci curvature condition
Ling Wu, Xingyu Song, Meng Zhu
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 eigenvalu…