The Bernstein problem and the classification of complete stable area-stationary surfaces in the Heisenberg group
César Rosales Universidad de Granada
We first consider the problem of finding all the entire area-stationary graphs in the sub-Riemannian Heisenberg group .This question has been well studied for t-graphs and for intrinsicgraphs. In particular, examples of unstable entire area-stationary graphs may be given in . After discussing some stability results for complete graphs we state a joint result with A. Hurtado and M. Ritoré, where we prove that a complete stable area-stationary surface in must be a Euclidean plane or congruent to the hyperbolic paraboloid .