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http://dx.doi.org/10.4134/CKMS.2005.20.4.775

STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION  

HWang, Seung-Su (Department of Mathematics Chung-Ang University)
Publication Information
Communications of the Korean Mathematical Society / v.20, no.4, 2005 , pp. 775-779 More about this Journal
Abstract
On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).
Keywords
critical point equation; stable minimal hypersurface;
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