5 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.…
Stochastic Curve Shortening Flow with Scale-Dependent Noise
Qi Yan
In this paper, we study the motion by mean curvature of curves in the plane perturbed by scale-dependent noise. We first introduce a so-called scale-dependent noise from the physic…
Maximal Solutions and Stochastic Free Boundary Formulations for Stochastic Willmore and Surface Diffusion Flows on
Qi Yan
We study the stochastic Willmore flow and the stochastic surface diffusion flow for closed or non-closed curves on in this paper. We equivalently formulate them as a…
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…