Singularities of surfaces defined by Monge-Ampere equations of hyperbolic type

In [18], we studied the singularities of solutions of Monge-Ampere equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: I) What kinds of singularities may appear ? and II) How can we extend the surfaces beyond the singularities ?