  In this paper we prove some results concerning stability of hypersurfaces in
the four dimensional Euclidean space with zero scalar curvature. First we prove
there is no complete stable hypersurface with zero scalar curvature, polynomial
growth of integral of the mean curvature, and with the Gauss-Kronecker
curvature bounded away from zero. We conclude this paper giving a sufficient
condition for a regular domain to be stable in terms of the mean and the
Gauss-Kronecker curvatures of the hypersurface and the radius of the smallest
extrinsic ball which contains the domain.
