Convex function on pseudo-Grassmann manifold and its applications for Bernstein-type theorem

Abstract

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

Keywords

Pseudo-Euclidean space / pseudo-Grassmann manifold / Bernstein-type theorem

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