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A Bernstein type theorem for minimal volume preserving maps
Author(s):
Lei
Ni
Journal:
Proc. Amer. Math. Soc.
130
(2002),
1207-1210.
MSC (2000):
Primary 58E20
Posted:
November 9, 2001
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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.
References:
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Additional Information:
Lei
Ni
Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305
Email:
lni@math.stanford.edu
DOI:
10.1090/S0002-9939-01-06448-6
PII:
S 0002-9939(01)06448-6
Keywords:
Minimal maps,
volume preserving,
lagrangian submanifolds
Received by editor(s):
August 18, 2000
Posted:
November 9, 2001
Additional Notes:
This research was partially supported by an NSF grant.
Communicated by:
Bennett Chow
Copyright of article:
Copyright
2001,
American Mathematical Society
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