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Convex functions on Grassmannian manifolds and Lawson–Osserman problem

Authors :
Xin, Y.L.
Yang, Ling
Source :
Advances in Mathematics. Nov2008, Vol. 219 Issue 4, p1298-1326. 29p.
Publication Year :
2008

Abstract

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; ]. In this way, the result for Bernstein type theorem done by Jost and the first author could be improved. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
00018708
Volume :
219
Issue :
4
Database :
Academic Search Index
Journal :
Advances in Mathematics
Publication Type :
Academic Journal
Accession number :
34302206
Full Text :
https://doi.org/10.1016/j.aim.2008.06.015