From Constant mean Curvature Hypersurfaces to the Gradient Theory of Phase Transitions
From Constant mean Curvature Hypersurfaces to the Gradient Theory of Phase Transitions
Given a nondegenerate minimal hypersurface Σ in a Riemannian manifold, we prove that, for all ε small enough there exists uε, a critical point of the Allen-Cahn energy Eε(u) = ε2 ∫ |∇u|2 + ∫(1 − u2)2, whose nodal set converges to Σ as ε tends to 0. Moreover, if …