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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…