Stability and eigenvalue estimates of linear Weingarten hypersurfaces in a sphere
نویسندگان
چکیده
منابع مشابه
Linear Weingarten hypersurfaces in a unit sphere
In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].
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in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].
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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: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.08.003