4 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…
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…
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…