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arXiv · 2111.06695

Second-order generalized Monge--Amp\`ere equations on a plane and its geometric singular solutions

Masahiro Kawamata
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Abstract

In the present paper, we study some generalized Monge--Amp\`ere equations in terms of special exterior differential systems on a jet space. Moreover, we construct geometric singular solutions of the generalized Monge--Amp\`ere 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.

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Masahiro Kawamata. 2021-11-12. Second-order generalized Monge--Amp\`ere equations on a plane and its geometric singular solutions. https://arxiv.org/abs/2111.06695

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