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Rigidity of 3D
spherical caps via $\mu$-bubbles
Yuhao Hu, Peng Liu and Yuguang Shi |
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Vol. 323 (2023), No. 1, 89–114
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DOI: 10.2140/pjm.2023.323.89
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Abstract |
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By using Gromov’s -bubble technique, we show that the -dimensional spherical caps are rigid under perturbations that do not reduce the metric, the scalar curvature, and the mean curvature along its boundary. Several generalizations of this result will be discussed. |
Keywords
Llarull's theorem, spherical cap, $ \mu$-bubble
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Mathematical Subject Classification
Primary: 53C21
Secondary: 53C24
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Milestones
Received: 27 May 2022
Revised: 23 January 2023
Accepted: 25 March 2023
Published: 29 May 2023
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Authors |
| Yuhao Hu | |
| Key Laboratory of Pure and Applied
Mathematics Peking University Beijing China |
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| Peng Liu | |
| Key Laboratory of Pure and Applied
Mathematics Peking University Beijing China |
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| Yuguang Shi | |
| Key Laboratory of Pure and Applied
Mathematics, School of Mathematical Sciences Peking University Beijing China |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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