Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 58E20

Retrieve articles in all journals with MSC (2000): 58E20


Additional Information

Lei Ni
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: lni@math.stanford.edu

DOI: http://dx.doi.org/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
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