We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [M...We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.展开更多
文摘We derive the Hessian estimate of the w-function defined on the pseudo-Grassmann manifold Gnmm, which is convex by the estimate. As an application, we give a direct proof of the Bernstein-type theorem due to Y. Xin [Mannscripta Math., 2000, 103： 191-202]. We also estimate the squared norm of the second fundamental form of a complete spacelike submanifold in pseudoEuclidean space in terms of the w-function and the mean curvature.
