Compactness analysis for free boundary minimal hypersurfaces
arXiv:1705.06255
Abstract
We investigate compactness phenomena involving free boundary minimal hypersurfaces in Riemannian manifolds of dimension less than eight. We provide natural geometric conditions that ensure strong one-sheeted graphical subsequential convergence, discuss the limit behaviour when multi-sheeted convergence happens and derive various consequences in terms of finiteness and topological control.
final version, to appear in Calc. Var. Partial Differential Equations