Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Abstract

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.

17 pages, 1 figure, revised version

Cited by in corpus (1)

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