Properties In A Space Of Constant Curvature Of Submanifolds With Constant Mean Curvature

The classical Bernstein type theorem is complete minimal graph must be hyperplane. This paper mainly studies the spatial Euclidean complete MinimalSubmanifolds in constant curvature and (1and-1) Hypersurfaces in Riemannmanifold, in a similar inequality conditions of stability, asymptotic estimation throughthe norm of the second fundamental form on the manifold long square, in constantcurvature space we get similar to the Bernstein type theorem. This paper is structuredas follows:In the first chapter, we list the main results obtained and preliminaryknowledge.In the second chapter, similar stability inequalities in the Euclidean space, weobtain a Bernstein type theorem.In the third chapter, under certain conditions, we obtain the constant curvature1hypersurface in the space to be totally umbilical.In the fourth chapter, under certain conditions, we obtain the constant curvaturespace-1is totally umbilical hypersurfaces.This paper generalizes the Li H. Z and Wei G. X theorem and S.Ilias,B.Nelliptical and M.Soret theorem.