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http://dx.doi.org/10.4134/CKMS.2008.23.4.587

SOME REMARKS ON STABLE MINIMAL SURFACES IN THE CRITICAL POINT OF THE TOTAL SCALAR CURVATURE  

Hwang, Seung-Su (DEPARTMENT OF MATHEMATICS CHUNG-ANG UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.4, 2008 , pp. 587-595 More about this Journal
Abstract
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics. When the domain of S is restricted to the space of constant scalar curvature metrics, there has been a conjecture that a critical point is isometric to a standard sphere. In this paper we investigate the relationship between the first Betti number and stable minimal surfaces, and study the analytic properties of stable minimal surfaces in M for n = 3.
Keywords
total scalar curvature; critical points; stable minimal surfaces;
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Times Cited By KSCI : 1  (Citation Analysis)
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