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A Bernstein type theorem for minimal volume preserving maps

Author: Lei Ni
Journal: Proc. Amer. Math. Soc. 130 (2002), 1207-1210
MSC (2000): Primary 58E20
Published electronically: November 9, 2001
MathSciNet review: 1873798
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Abstract: We show that any minimal volume preserving map from the Euclidean plane into itself is a linear diffeomorphism. We derive this from a similar result on minimal diffeomorphisms. We also show that the classical Bernstein theorem on minimal graphs is a corollary of our result.

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Additional Information

Lei Ni
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305

Keywords: Minimal maps, volume preserving, lagrangian submanifolds
Received by editor(s): August 18, 2000
Published electronically: November 9, 2001
Additional Notes: This research was partially supported by an NSF grant.
Communicated by: Bennett Chow
Article copyright: © Copyright 2001 American Mathematical Society