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A new convergence
theorem for mean curvature flow of hypersurfaces in
quaternionic projective spaces
Shiyang Li, Hongwei Xu and Entao Zhao |
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Vol. 332 (2024), No. 2, 219–241
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Abstract |
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We investigate the smooth convergence of the mean curvature flow of hypersurfaces in the quaternionic projective spaces. We prove that if the initial hypersurface satisfies a new nonlinear curvature pinching condition, then the mean curvature flow converges smoothly to a round point in finite time. Our result improves a smooth convergence theorem due to Pipoli and Sinestrari (2017). |
Keywords
mean curvature flow, convergence theorem, curvature
pinching, real hypersurfaces, quaternionic projective
spaces
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Mathematical Subject Classification
Primary: 53E10
Secondary: 53C40
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Milestones
Received: 18 March 2024
Revised: 16 July 2024
Accepted: 7 October 2024
Published: 6 December 2024
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Authors |
| Shiyang Li | |
| Center of Mathematical
Sciences Zhejiang University Hangzhou China |
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| Hongwei Xu | |
| Center of Mathematical
Sciences Zhejiang University Hangzhou China |
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| Entao Zhao | |
| Center of Mathematical
Sciences Zhejiang University Hangzhou China |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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