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Nets of lines depending on a parameter and sufficient conditions for their convergence

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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.

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Authors
  1. E. R. Rozendorn
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Translated fromItogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 22, 1990, pp. 3–36.

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Rozendorn, E.R. Nets of lines depending on a parameter and sufficient conditions for their convergence. J Math Sci 55, 1929–1953 (1991). https://doi.org/10.1007/BF01095670

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