New examples of Calabi¯Bernstein problems for some nonlinear equations

All the entire solutions to the maximal surface equation in certain 3-dimensional Lorentzian manifolds, obeying the null energy condition, are obtained. Thus, we solve new Calabi¯Bernstein problems. As a consequence, the corresponding parametric versions are also given. The behaviour of this Calabi¯Bernstein property with respect to an special family of C2 -perturbations of Lorentz¯Minkowski space L3 is investigated