Abstract
\«\dV £ cm, (1) M where cm denotes the area of a unit m-sphere. The equality sign of (1) holds when and only when M is a hypersphere in E. In order to know whether the inequality (1) can be improved for some given hypersurfaces in E, it is important to know the S-hypersurfaces in E, i.e., the stable hypersurfaces in E with respect to the integral ot!dV. The main purpose of this paper is to study the S-hypersurfaces in E. In §1, we obtain a necessary and sufficient condition for S-hypersurfaces in terms of mean curvature and scalar curvature. In §2, we obtain two applications.
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