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Convex function on pseudo-Grassmann manifold and its applications for Bernstein-type theorem |
Zicheng ZHAO( ) |
| Institute of Mathematics, Fudan University, Shanghai 200433, China |
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Abstract We derive the Hessian estimate of the ω-function defined on the pseudo-Grassmann manifold Gn,mm, 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.
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| Keywords
Pseudo-Euclidean space
pseudo-Grassmann manifold
Bernsteintype theorem
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Corresponding Author(s):
ZHAO Zicheng,Email:071018016@fudan.edu.cn
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Issue Date: 01 June 2012
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