Entire Solutions of the Allen-Cahn equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in ${\mathbb{R}}^3$

Manuel del Pino, Mike Kowalczyk, Juncheng Wei

We consider minimal surfaces $M$ which are complete, embedded and have finite total curvature in ${\mathbb{R}}^3$, and bounded, entire solutions with finite Morse index of the Allen-Cahn equ…