Minimal surfaces and the Allen--Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
Minimal surfaces and the Allen--Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
The Allen--Cahn equation is a semilinear PDE which is deeply linked to the theory of minimal hypersurfaces via a singular limit. We prove curvature estimates and strong sheet separation estimates for stable solutions (building on recent work of Wang--Wei) of the Allen--Cahn equation on a 3-manifold. Using these, we are …