Solution surfaces of Monge–Ampère equations

✍ Scribed by Go-o Ishikawa; Tohru Morimoto

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 92 KB
• Volume: 14
• Category: Article
• ISSN: 0926-2245
• DOI: 10.1016/s0926-2245(01)00033-x

✦ Synopsis

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 .