Shengwen Wang

activity

20172023

most citedWarped Tori with Almost Non-Negative Scalar Curvature

13 citations · 24 across the 9 of their papers we have counts for

collaborators

9 papers

math.DG2023

Quantization of the Energy for the inhomogeneous Allen-Cahn mean curvature

Huy The Nguyen, Shengwen Wang

We consider the varifold associated to the Allen--Cahn phase transition problem in $R^{n + 1}$ (or $n + 1$ -dimensional Riemannian manifolds with bounded curvature) with integral…

math.AP2020★ 3 cited

Brakke Regularity for the Allen-Cahn Flow

Huy The Nguyen, Shengwen Wang

In this paper we prove an analogue of the Brakke's $ε$ -regularity theorem for the parabolic Allen-Cahn equation. In particular, we show uniform $C^{2, α}$ regularity for t…

math.DG2020★ 2 cited

Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn

Huy The Nguyen, Shengwen Wang

The parabolic Allen-Cahn equation is a semilinear partial differential equation linked to the mean curvature flow by a singular perturbation. We show an improved convergence proper…

math.DG2019

Precise asymptotics near a generic $S^{1} \times R^{3}$ singularity of mean curvature flow

Zhou Gang, Shengwen Wang

In the present paper we study a type of generic singularity of mean curvature flow modelled on the bubble-sheet $S^{1} \times R^{3}$ , and we derive an asymptotic profile…

math.DG2018★ 13 cited

Warped Tori with Almost Non-Negative Scalar Curvature

Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise +2

For sequences of warped product metrics on a $3$ -torus satisfying the scalar curvature bound $R_{j} \geq - \frac{1}{j}$ , uniform upper volume and diameter bounds, and a uniform lower…

math.DG2018★ 5 cited

Low Entropy and the Mean Curvature Flow with Surgery

Alexander Mramor, Shengwen Wang

In this article, we extend the mean curvature flow with surgery to mean convex hypersurfaces with entropy less than $Λ_{n - 2}$ . In particular, 2-convexity is not assumed. Next we sh…

math.DG2018

The level set flow of a hypersurface in $R^{4}$ of low entropy does not disconnect

Jacob Bernstein, Shengwen Wang

We show that if $Σ \subset R^{4}$ is a closed, connected hypersurface with entropy $λ (Σ) \leq λ (S^{2} \times R)$ , then the level set flow of $Σ$ never disconnects…

math.DG2017★ 1 cited

On the topological rigidity of self shrinkers in $R^{3}$

Alexander Mramor, Shengwen Wang

In this note we show that compact self shrinkers in $R^{3}$ are "topologically standard" in that any genus $g$ compact self shrinker is ambiently isotopic to the standard ge…

math.DG2017

Round spheres are Hausdorff stable under small perturbation of entropy

Shengwen Wang

We show that if the entropy of any closed hypersurface is close to that of a round hyper-sphere, then it is close to a round sphere in Hausdorff distance. Generalizing the result o…

Quantization of the Energy for the inhomogeneous Allen-Cahn mean curvature

Brakke Regularity for the Allen-Cahn Flow

Second order estimates for transition layers and a curvature estimate for the parabolic Allen-Cahn

Precise asymptotics near a generic S1×R3 singularity of mean curvature flow

Warped Tori with Almost Non-Negative Scalar Curvature

Low Entropy and the Mean Curvature Flow with Surgery

The level set flow of a hypersurface in R4 of low entropy does not disconnect

On the topological rigidity of self shrinkers in R3

Round spheres are Hausdorff stable under small perturbation of entropy

Precise asymptotics near a generic $S^{1} \times R^{3}$ singularity of mean curvature flow

The level set flow of a hypersurface in $R^{4}$ of low entropy does not disconnect

On the topological rigidity of self shrinkers in $R^{3}$