Solution surfaces of Monge–Ampère equations

Abstract

In this paper we examine the singularities of solution surfaces of Monge–Ampère equations and study their global and local effects on the solutions for certain kinds of equations in the framework of contact geometry. In particular, as a byproduct, we give a simple proof to the classical Hartman–Nirenberg's theorem by using the notion of projective duality and provide a new example of compact developable hypersurfaces in the real projective space RP 4