14 citations · 56 across the 19 of their papers we have counts for
21 papers
Allard Regularity for Abelian Yang--Mills--Higgs Equation
Huy The Nguyen, Shengwen Wang
We study solutions to the self-dual Abelian Yang--Mills--Higgs (YMH) equations in the singular limit $\e \to 0 $, where the associated self-dual Ginzburg--Landau type energy \begin…
High Codimension Curve Shortening Flow with Free Boundary
Huy The Nguyen, Artemis A. Vogiatzi
We study curve shortening flow in high codimension for arcs with free boundary meeting a fixed smooth barrier orthogonally. We prove dilation-invariant curvature and higher-derivat…
Singularity Models for High Codimension Mean Curvature Flow in Riemannian Manifolds
Artemis A. Vogiatzi, Huy T. Nguyen
We study the mean curvature flow of smooth -dimensional compact submanifolds with quadratic pinching in a Riemannian manifold . Our main focus is on the case…
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 (or -dimensional Riemannian manifolds with bounded curvature) with integral…
Noncompact self-shrinkers for mean curvature flow with arbitrary genus
Reto Buzano, Huy The Nguyen, Mario B. Schulz
In his lecture notes on mean curvature flow, Ilmanen conjectured the existence of noncompact self-shrinkers with arbitrary genus. Here, we employ min-max techniques to give a rigor…
Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery
Mat Langford, Stephen Lynch, Huy The Nguyen
We study mean curvature flow of -dimensional submanifolds of , the round -sphere of sectional curvature , under the quadratic curvature pinching con…
Brakke Regularity for the Allen-Cahn Flow
Huy The Nguyen, Shengwen Wang
In this paper we prove an analogue of the Brakke's -regularity theorem for the parabolic Allen-Cahn equation. In particular, we show uniform regularity for t…
Sharp pinching estimates for mean curvature flow in the sphere
Mat Langford, Huy The Nguyen
We prove a suite of asymptotically sharp quadratic curvature pinching estimates for mean curvature flow in the sphere which generalize Simons' rigidity theorem for minimal hypersur…
Quadratically pinched hypersurfaces of the sphere via mean curvature flow with surgery
Mat Langford, Huy The Nguyen
We study mean curvature flow in , the round sphere of sectional curvature , under the quadratic curvature pinching condition $|A|^{2} < \frac{1}{n-2} H^{2}…
Convexity Estimates for High Codimension Mean Curvature Flow
Stephen Lynch, Huy The Nguyen
We consider the evolution by mean curvature of smooth -dimensional submanifolds in which are compact and quadratically pinched. We will be primarily intereste…
Evolving Pinched Submanifolds of the Sphere by Mean Curvature Flow
Charles Baker, Huy The Nguyen
In this paper, we prove convergence of the high codimension mean curvature flow in the sphere to either a round point or a totally geodesic sphere assuming a pinching condition bet…
High Codimension Mean Curvature Flow with Surgery
Stephen Lynch, Huy The Nguyen
We construct a mean curvature flow with surgery for submanifolds of arbitrary codimension. The theory applies to closed submanifolds satisfying a natural quadratic pinching conditi…
Cylindrical Estimates for High Codimension Mean Curvature Flow
Huy The Nguyen
We study high codimension mean curvature flow of a submanifold of dimension in Euclidean space subject to the quadratic curvature condition $…
Pinched Ancient Solutions to the High Codimension Mean Curvature Flow
Stephen Lynch, Huy The Nguyen
We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose…
The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds
Reto Buzano, Huy The Nguyen
In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points…
Surfaces of Co-dimension Two Pinched by Normal Curvature
Charles Baker, Huy The Nguyen
We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature are smoothly deformed by mean curvature flow to round points.
The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds
Reto Buzano, Huy The Nguyen
We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of C…
Global Conformal Invariants of Submanifolds
Andrea Mondino, Huy The Nguyen
The goal of the present paper is to investigate the algebraic structure of global conformal invariants of submanifolds. These are defined to be conformally invariant integrals of g…
Quantitative rigidity results for conformal immersions
Tobias Lamm, Huy The Nguyen
In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in with bounded total curvature. We show that (branched) conformal…
A Gap Theorem for Willmore Tori and an application to the Willmore Flow
Andrea Mondino, Huy The Nguyen
In 1965 Willmore conjectured that the integral of the square of the mean curvature of a torus immersed in is at least and attains this minimal value if and only if the…
Branched Willmore Spheres
Tobias Lamm, Huy The Nguyen
In this paper we classify branched Willmore spheres with at most three branch points (including multiplicity), showing that they may be obtained from complete minimal surfaces in $…