4 papers
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…
On mean curvature flow translators with prescribed ends
Ao Sun, Zhihan Wang
Given a smooth closed embedded self-shrinker with index in , we construct an -dimensional family of complete translators polynomially asymptotic to $S\ti…
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…
Genus one singularities in mean curvature flow
Adrian Chun-Pong Chu, Ao Sun
We show that for certain one-parameter families of initial conditions in , when we run mean curvature flow, a genus one singularity must appear in one of the flows. Mo…