Ambrozio, L, Carlotto, A and Sharp, B orcid.org/0000-0002-7238-4993 (2016) Compactness of the Space of Minimal Hypersurfaces with Bounded Volume and p-th Jacobi Eigenvalue. Journal of Geometric Analysis, 26 (4). pp. 2591-2601. ISSN 1050-6926
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015, Mathematica Josephina, Inc. This is a post-peer-review, pre-copyedit version of an article published in Journal of Geometric Analysis. The final authenticated version is available online at: https:// doi.org/10.1007/s12220-015-9640-4. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Minimal submanifolds; Compactness; Jacobi operator |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 Jul 2018 08:03 |
Last Modified: | 18 Jul 2018 08:03 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s12220-015-9640-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132673 |