9 citations · 54 across the 26 of their papers we have counts for
8 papers · 1 filter
On the Entropy of Parabolic Allen-Cahn Equation
Ao Sun
We define a (mean curvature flow) entropy for Radon measures in or in a compact manifold. Moreover, we prove a monotonicity formula of the entropy of the measures as…
Compactness of self-shrinkers in with fixed genus
Ao Sun, Zhichao Wang
We prove the compactness of self-shrinkers in with bounded entropy and fixed genus. As a corollary, we show that numbers of ends of such surfaces are uniformly bounde…
Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces
Ao Sun
In this paper we prove that the generic singularities of mean curvature flow of closed embedded surfaces in modeled by closed self-shrinkers with multiplicity has mul…
Singularities of Mean Curvature Flow of Surfaces with Additional Forces
Ao Sun
In this paper we study the blow up sequence of mean curvature flow of surfaces in with additional forces. We prove that the blow up limit of a mean curvature flow of…
Sharp Entropy Bounds for Plane Curves and Dynamics of the Curve Shortening Flow
Julius Baldauf, Ao Sun
We prove that a closed immersed plane curve with total curvature has entropy at least times the entropy of the embedded circle, as long as it generates a type I singulari…
Min-max minimal disks with free boundary in Riemannian manifolds
Longzhi Lin, Ao Sun, Xin Zhou
In this paper, we establish a min-max theory for constructing minimal disks with free boundary in any closed Riemannian manifold. The main result is an effective version of the par…
Compactness of Constant Mean Curvature Surfaces in Three Manifold with Positive Ricci Curvature
Ao Sun
In this paper we prove a compactness theorem for constant mean curvature surfaces with area and genus bound in three manifold with positive Ricci curvature. As an application, we g…
Compactness and Rigidity of -Surfaces
Ao Sun
In this paper we develop the compactness theorem for -surface in with uniform , genus, and area growth. This theorem can be viewed as a generalization of Coldin…