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$ F$-stability of $ f$-minimal hypersurface


Authors: Weimin Sheng and Haobin Yu
Journal: Proc. Amer. Math. Soc. 143 (2015), 3619-3629
MSC (2010): Primary 53C21; Secondary 53C23
DOI: https://doi.org/10.1090/proc/12514
Published electronically: April 23, 2015
MathSciNet review: 3348803
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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.


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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

DOI: https://doi.org/10.1090/proc/12514
Keywords: $F$-stability, $f$-minimal hypersurface, gradient Ricci soliton
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
Article copyright: © Copyright 2015 American Mathematical Society