Second-order generalized Monge--Ampère equations on a plane and its geometric singular solutions

2021/11/12 by Kawamata, Masahiro
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.06695

Abstract

In the present paper, we study some generalized Monge--Ampère equations in terms of special exterior differential systems on a jet space. Moreover, we construct geometric singular solutions of the generalized Monge--Ampère equations by using the method of Cauchy characteristics. Furthermore, we give criteria for geometric singular solutions to be right-left equivalent to the cuspidal edge, swallowtail and butterfly.

Related

• On a generalization of Monge-Ampère equations and Monge-Ampère systems
• Entire solutions of the degenerateMonge-Ampere equation with a finite\n number of singularities
• Symmetry Results for classical solutions of Monge-Ampere system in the plane
• Some remarks on contact manifolds, Monge-Ampere equations and solution singularities
• Some Remarks on Multisymplectic and Variational Nature of Monge-Ampère Equations in Dimension Four