On the Cauchy problem for the integrable system of Lie -minimal surfaces

In this paper we apply the Cartan-Kähler theory of exterior differential systems to solve the Cauchy problem for the integrable system of Lie minimal surfaces and discuss the underlying geometry. One purpose for this work is to show how methods and language from the theory of exterior differential systems may prove to be useful in the study of real analytic initial value problems, especially for gaining insight into the geometric aspects of the initial conditions and the solutions.