STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION

Title & Authors
STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION
HWang, Seung-Su;

Abstract
On a compact n-dimensional manifold $\small{M^n}$, 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 $\small{Z_g\;=\;s_g^{1\ast}(f)}$. 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 $\small{M^n}$ under an assumption that Ker($\small{s_g^{1\ast}{\neq}0}$).ﾖ⨀
Keywords
critical point equation;stable minimal hypersurface;
Language
English
Cited by
1.
TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES,;

호남수학학술지, 2008. vol.30. 4, pp.677-683
2.
SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE,;

대한수학회논문집, 2008. vol.23. 4, pp.587-595
1.
TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES, Honam Mathematical Journal, 2008, 30, 4, 677
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