Barbosa, E, Sharp, B orcid.org/0000-0002-7238-4993 and Wei, Y (2017) Smooth compactness of ƒ-minimal hypersurfaces with bounded ƒ-index. Proceedings of the American Mathematical Society, 145 (11). pp. 4945-4961. ISSN 0002-9939
Abstract
Let (Mⁿ⁺¹, g, e−ƒ dμ) be a complete smooth metric measure space with 2 ≤ n ≤ 6 and Bakry-Émery Ricci curvature bounded below by a positive constant. We prove a smooth compactness theorem for the space of complete embedded ƒ-minimal hypersurfaces in M with uniform upper bounds on ƒ-index and weighted volume. As a corollary, we obtain a smooth compactness theorem for the space of embedded self-shrinkers in Rⁿ⁺¹ with 2 ≤ n ≤ 6. We also prove some estimates on the ƒ-index of ƒ-minimal hypersurfaces.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 American Mathematical Society. This is an author produced version of a paper published in the Proceedings of the American Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy. |
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: | 27 Jun 2018 09:37 |
Last Modified: | 28 Jun 2018 03:46 |
Status: | Published |
Publisher: | American Mathematical Society |
Identification Number: | 10.1090/proc/13628 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132570 |