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The structure of weakly stable minimal hypersurfaces

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Author(s): Cheng Xu | Cheung Leung-Fu | Zhou Detang

Journal: Anais da Academia Brasileira de Ciências
ISSN 0001-3765

Volume: 78;
Issue: 2;
Start page: 195;
Date: 2006;
Original page

Keywords: minimal hypersurfaces | weak stability | ends

ABSTRACT
In this short communication, we announce results from our research on the structure of complete noncompact oriented weakly stable minimal hypersurfaces in a manifold of nonnegative sectional curvature. In particular, a complete oriented weakly stable minimal hypersurface in Rm, m > 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one end if the complete oriented ambient manifold Nm, m > 7, has nonnegative sectional curvature and Ricci curvature bounded below by a positive constant; a complete oriented weakly stable minimal hypersurface in Rm, m > 4, with finite total scalar curvature is a hyperplane.
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