Title: Dual quadratic differentials and entire minimal graphs in Heisenberg space,
Abstract: We define holomorphic quadratic differentials for spacelike surfaces with
constant mean curvature in the Lorentzian homogeneous spaces
$\mathbb{L}(\kappa,\tau)$ with isometry group of dimension 4, which are dual to
the Abresch-Rosenberg differentials in the Riemannian counterparts
$\mathbb{E}(\kappa,\tau)$, and obtain some consequences. On the one hand, we
give a very short proof of the Bernstein problem in Heisenberg space, and
provide a geometric description of the family of entire graphs sharing the same
differential in terms of a 2-parameter conformal deformation. On the other
hand, we prove that entire minimal graphs in Heisenberg space have negative
Gauss curvature.