
The Hidden Interface That Forces a 3D Equation to Flatten
A proof turns the Allen–Cahn equation’s hidden interface into a geometric trap, ruling out curved stable fronts in three dimensions.

A proof turns the Allen–Cahn equation’s hidden interface into a geometric trap, ruling out curved stable fronts in three dimensions.

A new theorem shows how a hidden two-dimensional coordinate change can reveal smoothness in rough geometric graphs, even in high codimension.