Eigenvalue estimates for stable minimal hypersurfaces
نویسندگان
چکیده
منابع مشابه
The structure of weakly stable minimal hypersurfaces.
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 > or = 4, must have only one end; any complete noncompact oriented weakly stable minimal hypersurface has only one e...
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ABSTRACT : The stability operator of a compact oriented minimal hypersurface Mn−1 ⊂ S is given by J = −∆ − ‖A‖ − (n − 1), where ‖A‖ is the norm of the second fundamental form. Let λ1 be the first eigenvalue of J and define β = −λ1 − 2(n − 1). In [S] Simons proved that β ≥ 0 for any non-equatorial minimal hypersurface M ⊂ S. In this paper we will show that β = 0 only for Clifford hypersurfaces. ...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2012
ISSN: 1331-4343
DOI: 10.7153/mia-15-07