Given a closed Riemannian manifold of dimension 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≥ 2 one gains strong convergence to a smooth limit submanifold away from at most p- 1 points.
Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue / Ambrozio, L.; Carlotto, A.; Sharp, B.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 26:4(2016), pp. 2591-2601. [10.1007/s12220-015-9640-4]
Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue
Carlotto A.;
2016-01-01
Abstract
Given a closed Riemannian manifold of dimension 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≥ 2 one gains strong convergence to a smooth limit submanifold away from at most p- 1 points.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
