We show that the mean curvature flow of generic closed surfaces in\(\mathbb {R}^{3}\)
avoids asymptotically conical and non-spherical compact singularities. We also show that …

In this paper, we study the dynamics of the mean curvature flow approaching a cylindrical
singularity and show that generically such a singularity is nondegenerate, robust, and …

This is a contribution to the program of dynamical approach to mean curvature flow initiated
by Colding and Minicozzi. In this paper, we prove two main theorems. The first one is local in …

This is the second paper in the series to study the initial perturbation of mean curvature flow.
We study the initial perturbation of mean curvature flow, whose first singularity is modeled by …

Compactness of self-shrinkers in R3 with fixed genus - ScienceDirect Skip to main contentSkip
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In this paper, we show that if the mean curvature of a closed smooth embedded mean
curvature flow in R3 is of type-I, then the rescaled flow at the first finite singular time …

Mean curvature flow is the most natural evolution equation in extrinsic geometry, and shares
many features with Hamilton's Ricci flow from intrinsic geometry. In this lecture series, I will …

The entropy of a hypersurface is defined by the supremum over all Gaussian integrals with
varying centers and scales, thus invariant under rigid motions and dilations. It measures …

We define a local (mean curvature flow) entropy for Radon measures in Rn or in a compact
manifold. Moreover, we prove a monotonicity formula of the entropy of the measures …

“An analytical approach to many problems in geometry leads to the study of partial
differential equations.”(AV Pogorelov, Foreword to The Minkowski Multidimensional …