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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Curvature estimates for minimal submanifolds of higher codimension and small G-rank


Authors: J. Jost, Y. L. Xin and Ling Yang
Journal: Trans. Amer. Math. Soc. 367 (2015), 8301-8323
MSC (2010): Primary 58E20, 53A10
DOI: https://doi.org/10.1090/tran/6782
Published electronically: September 2, 2015
MathSciNet review: 3403056
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Abstract: We obtain new curvature estimates and Bernstein type results for a minimal $ n-$submanifold in $ \mathbb{R}^{n+m},\, m\ge 2$, under the condition that the rank of its Gauss map is at most 2. In particular, this applies to minimal surfaces in Euclidean spaces of arbitrary codimension.


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Additional Information

J. Jost
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany — and — Department of Mathematics, University of Leipzig, 04081 Leipzig, Germany
Email: jost@mis.mpg.de

Y. L. Xin
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: ylxin@fudan.edu.cn

Ling Yang
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Email: yanglingfd@fudan.edu.cn

DOI: https://doi.org/10.1090/tran/6782
Received by editor(s): October 4, 2012
Published electronically: September 2, 2015
Additional Notes: The first author was supported by the ERC Advanced Grant FP7-267087
The second and third authors were supported partially by NSFC. They are also grateful to the Max Planck Institute for Mathematics in the Sciences in Leipzig for its hospitality and continuous support
Article copyright: © Copyright 2015 American Mathematical Society

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