F F -stability of f f -minimal hypersurface

F F -stability of f f -minimal hypersurface

In this paper we study the classification of the ff-minimal hypersurface immersed in the manifold Mn×RM^{n}\times R, where (Mn,g)(M^{n}, g) is an Einstein manifold with positive Ricci curvature. By using the FF functional and FF-stability which were introduced by Huisken and Colding-Minicozzi respec...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2015-04, Vol.143 (8), p.3619-3629
Hauptverfasser: Sheng, Weimin, Yu, Haobin
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Yu, Haobin
description In this paper we study the classification of the ff-minimal hypersurface immersed in the manifold Mn×RM^{n}\times R, where (Mn,g)(M^{n}, g) is an Einstein manifold with positive Ricci curvature. By using the FF functional and FF-stability which were introduced by Huisken and Colding-Minicozzi respectively, we prove that among all complete ff-minimal hypersurfaces with polynomial volume growth, only Mn×{0}M^{n}\times \{0\} is FF-stable.
doi_str_mv 10.1090/proc/12514
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title F F -stability of f f -minimal hypersurface
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