JOURNAL BROWSE
Search
Advanced SearchSearch Tips
STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
STABLE MINIMAL HYPERSURFACES IN A CRITICAL POINT EQUATION
HWang, Seung-Su;
  PDF(new window)
 Abstract
On a compact n-dimensional manifold , 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 . 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 under an assumption that Ker().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 crossref(new window)
2.
SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE,;

대한수학회논문집, 2008. vol.23. 4, pp.587-595 crossref(new window)
1.
TOTAL SCALAR CURVATURE AND EXISTENCE OF STABLE MINIMAL SURFACES, Honam Mathematical Journal, 2008, 30, 4, 677  crossref(new windwow)
 References
1.
A. L. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987

2.
A. E. Fischer and J. E. Marsden, Manifolds of Riemannian Metrics with Prescribed Scalar Curvature, Bull. Amer. Math. Soc. 80 (1974), 479-484 crossref(new window)

3.
S. Hwang, Critical points and conformally fiat metrics, Bull. Korean Math. Soc. 37 (2000), no. 3, 641-648

4.
S. Hwang, Critical points of the scalar curvature funetionals on the space of meirics of constant scalar curvature, Manuscripta Math. 103 (2000), 135-142 crossref(new window)

5.
S. Hwang, The critical point equation on a three dimensional compact manifold, Proc. Amer. Math. Soc. 131 (2003), 3221-3230 crossref(new window)

6.
H. B. Lawson, Minimal varieties in real and complex geometry, University of Montreal lecture notes, 1974