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math.DG2023
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…
math.DG2023
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…
math.DG2023★ 4 cited
Linear stability of compact shrinking Ricci solitons
Huai-Dong Cao, Meng Zhu
In this paper, we continue investigating the second variation of Perelman's -entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in…