| Abstract: | We study criteria for the global regularity of a net of lines defined on the plane or a part of it by an ordinary differential equation of first order and second degree, nets depending on a parameter, and questions of convergence on the parameter. We use an analytic technique connected with hyperbolic systems of equations of a special form. We give applications to surfaces of negative Gaussian curvature and to hyperbolic Monge-Ampère equations.Translated fromItogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 22, 1990, pp. 3–36. |
