Title: Boundary behavior of the Allen-Cahn equation and the construction of free boundary minimal hypersurfacesAbstract: In the late 70s, the work of Modica, Mortola, De Giorgi, and many others established deep connections between the Allen-Cahn equation, a semi-linear elliptic equation arising in the van der Waals-Cahn-Hilliard theory of phase transitions, and minimal hypersurfaces, i.e. critical […]