A Bernstein type theorem for minimal volume preserving maps

Ni, Lei

doi:10.1090/S0002-9939-01-06448-6

A Bernstein type theorem for minimal volume preserving maps
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Proc. Amer. Math. Soc. 130 (2002), 1207-1210 Request permission

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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