The extension and convergence of mean curvature flow in higher codimension
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- by Kefeng Liu, Hongwei Xu, Fei Ye and Entao Zhao PDF
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Abstract:
In this paper, we investigate the convergence of the mean curvature flow of closed submanifolds in $\mathbb {R}^{n+q}$. We show that if the initial submanifold satisfies some suitable integral curvature conditions, then along the mean curvature flow it will shrink to a round point in finite time.References
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Additional Information
- Kefeng Liu
- Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China – and – Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California, 90095-1555
- Email: kefeng@zju.edu.cn, liu@math.ucla.edu
- Hongwei Xu
- Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
- MR Author ID: 245171
- Email: xuhw@zju.edu.cn
- Fei Ye
- Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: yf@cms.zju.edu.cn, flemmingye@163.com
- Entao Zhao
- Affiliation: Center of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
- MR Author ID: 884026
- Email: zhaoet@zju.edu.cn
- Received by editor(s): September 23, 2016
- Received by editor(s) in revised form: January 23, 2017
- Published electronically: November 1, 2017
- Additional Notes: This research was supported by the National Natural Science Foundation of China, Grant Nos. 11531012, 11371315, 11201416.
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 2231-2262
- MSC (2010): Primary 53C44, 53C40
- DOI: https://doi.org/10.1090/tran/7281
- MathSciNet review: 3739208