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Convex functions on Grassmannian manifolds and Lawson-Osserman problem
Authors:YL Xin  Ling Yang
Institution:a Institute of Mathematics, Fudan University, Shanghai 200433, China
b Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), Ministry of Education, China
Abstract: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.
Keywords:49Q05  53A07  53A10
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