논문KCI 등재
Stable minimal hypersurfaces in a Critical Point Equation
대한수학회 (The Korean Mathematical Society)|2005.10|대한수학회논문집 (Communications of the KMS)|제20권 제4호|pp. 775-779
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Abstract
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.
참고문헌 (4)
- "Manifolds of Riemannian Metrics with Prescribed Scalar Curvature", 80, pp.479~484 (1974)
- "Critical points and conformally °at metrics", 37(3), pp.641~648 (2000)
- "Critical points of the scalar curvature functionals on the space of metrics of constant scalar curvature", 103, pp.135~142 (2000)
- "The critical point equation on a three dimensional compact manifold", 131, pp.3221~3230 (2003)
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