The indefinite affine Cauchy problem. (July 2020) - Milán, Francisco
Abstract: We solve the geometric Cauchy problem for the class of affine maximal surfaces, with indefinite affine metric, in the affine space R 3, that is, we find all the surfaces of this class which contain a given regular curve of R 3 with prescribed affine normal and affine conormal along it. 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 (asymptotic) directions. As application we obtain some results about geodesics and symmetries of indefinite affine maximal surfaces.