40 citations · 126 across the 29 of their papers we have counts for
30 papers
Harnack Inequality for -Mean Curvature Flow
Xiang-Dong Li, Qi Yan
In this paper, we prove a Li-Yau-Hamilton type Harnack estimate for the -mean curvature flow in Euclidean space, which can be viewed as a gradient flow of the weighed area funct…
Monotonicity of Perelman -Entropy of Mean Curvature Flow
Xiang-Dong Li, Qi Yan
In this paper, we study Perelman' s entropy for mean curvature flow in . Analogously to Perelman's -entropy defined for Ricci flow, K.…
Existence of martingale solutions for a stochastic weighted mean curvature flow of graphs
Qi Yan, Xiang-Dong Li
We are concerned with a stochastic mean curvature flow of graphs with extra force over a periodic domain of any dimension. Based on compact embedding method of variational SPDE, we…
-entropy formulas and Langevin deformation on the -Wasserstein space over Riemannian manifolds
Rong Lei, Xiang-Dong Li, Yu-Zhao Wang
We first prove the -entropy formula and rigidity theorem for the geodesic flow on the -Wasserstein space over a complete Riemannian manifold with bounded geometry condition…
On Perelman's -entropy and Shannon entropy power for super Ricci flows on metric measure spaces
Xiang-Dong Li
In this paper, we extend Perelman's -entropy formula and the concavity of the Shannon entropy power from smooth Ricci flow to super Ricci flows on metric measure spaces. Moreove…
On the -entropy and Shannon entropy power on RCD and RCD spaces
Xiang-Dong Li, Enrui Zhang
In this paper, we prove the -entropy formula and the monotonicity and rigidity theorem of the -entropy for the heat flow on RCD and RCD spaces ,…