𝐹-stability of 𝑓-minimal hypersurface

Sheng, Weimin; Yu, Haobin

doi:10.1090/proc/12514

$F$-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.

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