$F$-stability of $f$-minimal hypersurface
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- by Weimin Sheng and Haobin Yu PDF
- Proc. Amer. Math. Soc. 143 (2015), 3619-3629 Request permission
Abstract:
In this paper we study the classification of the $f$-minimal hypersurface immersed in the manifold $M^{n}\times R$, where $(M^{n}, g)$ is an Einstein manifold with positive Ricci curvature. By using the $F$ functional and $F$-stability which were introduced by Huisken and Colding-Minicozzi respectively, we prove that among all complete $f$-minimal hypersurfaces with polynomial volume growth, only $M^{n}\times \{0\}$ is $F$-stable.References
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Additional Information
- Weimin Sheng
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: weimins@zju.edu.cn
- Haobin Yu
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China
- Email: robin1055@126.com
- Received by editor(s): September 30, 2013
- Published electronically: April 23, 2015
- Additional Notes: The authors were supported by NSFC, grant no. 11131007, and Zhejiang provincial natural science foundation of China, grant no. LY14A010019.
- Communicated by: Lei Ni
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3619-3629
- MSC (2010): Primary 53C21; Secondary 53C23
- DOI: https://doi.org/10.1090/proc/12514
- MathSciNet review: 3348803