The geometric Cauchy problem for the hyperbolic Hessian one equation. (September 2015) - Martínez, Antonio; Milán, Francisco
Abstract: We solve the problem of finding all indefinite improper affine spheres passing through a given regular curve of R 3 with a prescribed affine co-normal vector field along this curve. We prove the problem is well-posed when the initial data are non-characteristic and show that uniqueness of the solution can fail at characteristic directions. As application we classify the indefinite improper affine spheres admitting a geodesic planar curve.