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Sharp Li-Yau type gradient estimates on hyperbolic spaces
Chengjie Yu, Feifei Zhao
In this paper, motivated by the works of Bakry et. al in finding sharp Li-Yau type gradient estimate for positive solutions of the heat equation on complete Riemannian manifolds wi…
Li-Yau multiplier set and optimal Li-Yau gradient estimate on hyperbolic spaces
Chengjie Yu, Feifei Zhao
In this paper, motivated by finding sharp Li-Yau type gradient estimate for positive solution of heat equations on complete Riemannian manifolds with negative Ricci curvature lower…
Heat kernel recurrence on space forms and applications
Chengjie Yu, Feifei Zhao
In this paper, we first give a direct proof for two recurrence relations of the heat kernels for hyperbolic spaces in \cite{DM}. Then, by similar computation, we give two similar r…
Affine Self-similar solutions of the affine curve shortening flow I: The degenerate case
Chengjie Yu, Feifei Zhao
In this paper, we consider affine self-similar solutions for the affine curve shortening flow in the Euclidean plane. We obtain the equations of all affine self-similar solutions u…
On the Li-Yau type gradient estimate of Li and Xu
Zhigang Chen, Chengjie Yu, Feifei Zhao
In this paper, we obtain a Li-Yau type gradient estimate with time dependent parameter for positive solutions of the heat equation, so that the Li-Yau type gradient estimate of Li-…