The Cauchy problem for a hyperbolic Monge-Ampère equation (Q1316879)

The author studies the Cauchy problem for a hyperbolic Monge-Ampère equation with two independent variables. He proves that any hyperbolic Monge-Ampère equation can be reduced to a system of five equations in Riemannian invariants. On the basis of this reduction he derives a lower estimate for the dimensions of the domain of existence of the solution to the Cauchy problem for a Monge-Ampère equation whose coefficients do not depend on the unknown function or its derivatives.