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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal graphs in $ \mathbb{R}^{4}$ with bounded Jacobians


Authors: Th. Hasanis, A. Savas-Halilaj and Th. Vlachos
Journal: Proc. Amer. Math. Soc. 137 (2009), 3463-3471
MSC (2000): Primary 53C42
Published electronically: May 8, 2009
MathSciNet review: 2515415
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Abstract: We obtain a Bernstein type result for entire two dimensional minimal graphs in $ \mathbb{R}^{4}$, which extends a previous result due to L. Ni. Moreover, we provide a characterization for complex analytic curves.


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Additional Information

Th. Hasanis
Affiliation: Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece
Email: thasanis@uoi.gr

A. Savas-Halilaj
Affiliation: Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece
Email: ansavas@cc.uoi.gr

Th. Vlachos
Affiliation: Department of Mathematics, University of Ioannina, 45110, Ioannina, Greece
Email: tvlachos@uoi.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09901-8
PII: S 0002-9939(09)09901-8
Keywords: Minimal surface, Bernstein type theorem, Jacobian
Received by editor(s): July 7, 2008
Received by editor(s) in revised form: January 27, 2009
Published electronically: May 8, 2009
Additional Notes: The second author was supported financially by the Foundation for Education and European Culture.
Communicated by: Richard A. Wentworth
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.