Bourni, T, Sharp, B orcid.org/0000-0002-7238-4993 and Tinaglia, G (2022) CMC hypersurfaces with bounded Morse index. Journal für die reine und angewandte Mathematik, 2022 (786). pp. 175-203. ISSN 0075-4102
Abstract
We provide qualitative bounds on the area and topology of separating constant mean curvature (CMC) surfaces of bounded (Morse) index. We also develop a suitable bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular, we show that convergence always occurs with multiplicity one, which implies that the minimal blow-ups (bubbles) are all catenoids.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Bourni, Sharp and Tinaglia, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. |
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: | 16 Mar 2022 15:16 |
Last Modified: | 29 Mar 2023 18:45 |
Status: | Published |
Publisher: | De Gruyter |
Identification Number: | 10.1515/crelle-2022-0009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:184786 |