Frontiers of Mathematics in China >
Convex function on pseudo-Grassmann manifold and its applications for Bernstein-type theorem
Received date: 10 Nov 2010
Accepted date: 28 Oct 2011
Published date: 01 Jun 2012
Copyright
We derive the Hessian estimate of the ω-function defined on the pseudo-Grassmann manifold , 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 ω-function and the mean curvature.
Zicheng ZHAO . Convex function on pseudo-Grassmann manifold and its applications for Bernstein-type theorem[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 597 -606 . DOI: 10.1007/s11464-012-0197-2
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