Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and <Emphasis Type="Italic">p</Emphasis>-th Jacobi Eigenvalue |
| |
Authors: | Lucas Ambrozio Alessandro Carlotto Ben Sharp |
| |
Institution: | 1.Department of Mathematics,Imperial College of Science and Technology,London,UK |
| |
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 \(p\ge 2\) one gains strong convergence to a smooth limit submanifold away from at most \(p-1\) points. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |