Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue
arXiv:1505.06652
Abstract
Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on the p-th Jacobi eigenvalue for p greater or equal than 2 one gains strong convergence to a smooth limit submanifold away from at most p-1 points.
final version, to appear on The Journal of Geometric Analysis