47 citations · 95 across the 21 of their papers we have counts for
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Mean curvature flows with cylindrical singularities II: stability and genericity
Ao Sun, Jinxin Xue
In [SX25], we introduced the notion of nondegenerate cylindrical singularity using the ideas from dynamical systems. In this paper, we further study the properties of these singula…
Generic mean curvature flows with cylindrical singularities I: the normal forms and nondegeneracy
Ao Sun, Jinxin Xue
This paper studies the dynamics of mean curvature flow as it approaches a cylindrical singularity. We proved that the rescaled mean curvature flow converging to a smooth generalize…
Generic regularity of Level Set Flows with spherical singularity
Ao Sun, Jinxin Xue
The sphere is well-known as the only generic compact shrinker for mean curvature flow (MCF). In this paper, we characterize the generic dynamics of MCFs with a spherical singularit…
Generic Dynamics of Mean Curvature Flows with Asymptotically Conical Singularities
Ao Sun, Jinxin Xue
This is the second paper in the series to study the generic dynamics of mean curvature flows. We study the initial perturbation of mean curvature flows, whose first singularity is…
Initial Perturbation of the Mean Curvature Flow for closed limit shrinker
Ao Sun, Jinxin Xue
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 l…