Related To The Bernstein Problem And Some Results

In this paper we study the Bernstein problem about higher codimension graph.Firstly,Bernstein type theorem about Hamiltonian minimal Lagrangian graph and the Lagrangian graph with conformal Maslov form,which both can be characterized by having partial harmonic Gauss map are established respectively.Then we define the admissible domain of a higher codimension minimal graph, and prove that one can only place finite admissible domain on/R~n disjointly.Finally,as a natural generation of minimal submanifolds,we study the biharmonic submanifolds.Namely,new examples of biharmonic submanifolds are constructed in cpn;classification results about biharmonic space-like hypersurface in 3-dimensional pseudo-Riemannian space and new examples in the ADS space are obtained;the rigidity of submanifolds whose Gauss map have vanishing biharmonic stress-energy tensor is studied.