Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Details Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

2007-05-10

arxiv.org/abs/0705.1436v2

Mathematics

Differential Geometry

17 pages, 1 figure, revised version

Scientific paper

We classify the entire minimal vertical graphs in the 3 dimensional
Heisenberg group Nil endowed with a Riemannian left-invariant metric. This
classification, which provides a solution to the Bernstein problem in Nil, is
given in terms of the Abresch-Rosenberg holomorphic differential for minimal
surfaces in Nil.

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