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

DOI:
https://doi.org/10.1090/S0002-9939-01-06448-6

Published electronically:
November 9, 2001

MathSciNet review:
1873798

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Abstract | References | Similar Articles | Additional Information

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

Email:
lni@math.stanford.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06448-6

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