Holomorphic quadratic differentials and the Bernstein problem in Heisenberg space

Abstract

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