Plateau's problem via the Allen--Cahn functional

Marco A. M. Guaraco, Stephen Lynch

Let $\Gamma$ be a compact codimension-two submanifold of ${\mathbb{R}}^n$, and let $L$ be a nontrivial real line bundle over $X={\mathbb{R}}^n\setminus \Gamma$. We study the Allen--Cahn funct…