9 citations · 54 across the 26 of their papers we have counts for
27 papers
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…
Rigidity and non-rigidity of the stable norm on
Fernando C. Marques, André Neves, Ao Sun
We show that the stable norm of flat metrics on is locally rigid if and locally rigid among metrics of the same volume if . We also sho…
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…
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 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…
Existence of minimal hypersurfaces with arbitrarily large area and possible obstructions
James Stevens, Ao Sun
We prove that in a closed Riemannian manifold with dimension between and , either there are minimal hypersurfaces with arbitrarily large area, or there exist uncountably man…
A Generalized Knockoff Procedure for FDR Control in Structural Change Detection
Jingyuan Liu, Ao Sun, Yuan Ke
Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of…
Rigidity of spherical product Ricci solitons
Ao Sun, Jonathan J. Zhu
We show that is isolated as a shrinking Ricci soliton in the space of metrics, up to scaling and diffeomorphism. We also prove the same rigidity for ,…
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…
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…
Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at
Douglas Stryker, Ao Sun
Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flo…
Admissibility of solution estimators for stochastic optimization
Amitabh Basu, Tu Nguyen, Ao Sun
We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of t…
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…