Convex functions on Grassmannian manifolds and Lawson-Osserman problem

被引：19
|
作者：
Xin, Y. L. [1 ,2 ]
Yang, Ling [1 ,2 ]
机构：
[1] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China
[2] Fudan Univ, Key Lab Math Nonlinear Sci, Minist Educ, Shanghai 200433, Peoples R China
来源：
ADVANCES IN MATHEMATICS | 2008年 / 219卷 / 04期
基金：
中国国家自然科学基金;
关键词：
convex function; Grassmannian manifold; Gauss map; Bernstein type theorem;
D O I：
10.1016/j.aim.2008.06.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We derive estimates of the Hessian of two smooth functions defined on Grassmannian manifold. Based on it, we can derive curvature estimates for minimal submanifolds in Euclidean space via Gauss map as in [Y.L. Xin, Ling Yang, Curvature estimates for minimal submanifolds of higher codimension, arXiv: 0709.3686; 24]. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved. (C) 2008 Elsevier Inc. All rights reserved.
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页码：1298 / 1326
页数：29
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