Minimal surfaces in three dimensional pseudo-Hermitian manifolds

We consider surfaces immersed in three-dimensional pseudo-Hermitian manifolds. A notion of pseudo mean curvature (p-mean curvature for short) is defined, which extends naturally some previous concepts given in the Heisenberg group. We derive this notion in different natural ways, which are all equivalent, and then study the p- minimal surface equation. Of great importance is the study of the singular set, which allows us to classify entire graphs in the Heisenberg group. Some applications of this result are then given, and some related issues are discussed.