Monge-Ampère equations and surfaces with negative Gaussian curvature
Tom 39 / 1997
Banach Center Publications 39 (1997), 161-170
DOI: 10.4064/-39-1-161-170
Streszczenie
In [24], we studied the singularities of solutions of Monge-Ampère 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: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?
