Stable minimal hypersurfaces in a Critical Point Equation

초록

On a compact n¡dimensional manifold Mn , a criti cal point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, sati .es the critical point equation (CPE), given by zg = s0¤g (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 Mn under an assumption that Ker(s0¤g ) = 0.

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