5 citations · 8 across the 3 of their papers we have counts for
15 papers
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…
Multiplicity one for min-max theory in compact manifolds with boundary and its applications
Ao Sun, Zhichao Wang, Xin Zhou
We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approa…
Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers
Ao Sun, Jonathan J. Zhu
We show that the product of two round shrinking spheres is an isolated self-shrinker in any codimension, modulo rotations. Moreover we prove explicit Łojasiewicz inequalities near…
Bifurcation of perturbations of non-generic closed self-shrinkers
Zhengjiang Lin, Ao Sun
We discover a bifurcation of the perturbations of non-generic closed self-shrinkers. If the generic perturbation is outward, then the next mean curvature flow singularity is cylind…
Entropy in A Closed Manifold and Partial Regularity of Mean Curvature Flow Limit of Surfaces
Ao Sun
Inspired by the idea of Colding-Minicozzi in [CM1], we define (mean curvature flow) entropy for submanifolds in a general ambient Riemannian manifold. In particular, this entropy i…
Construction of High Codimension Ancient Mean Curvature Flows
Douglas Stryker, Ao Sun
We construct a class of compact ancient solutions to the mean curvature flow in Euclidean space with high codimension. In particular, we construct higher codimensional ancient curv…