Applied singularity theory to exterior differential systems

得到了以下结果：Monge-Ampere方程几何解中类属奇点的分类。Goursat-Legendre对应关系的澄清。奇异勒让德子流形的基本研究，特别是奇异勒让德曲线。可展项的奇点分支。投射对偶下双退化子流形的估计。引进奇异余迷向映射的概念。辛模空间上局部化定理的证明。空间映射的基础研究。奇异勒让德纽结的分类理论。发现三维Monge-Ampere方程解的新奇点。单峰曲线奇点的分类及其辛模空间的确定。发现了平面曲线奇点的自同构分类与伴随Legendre曲线奇点的接触自同构分类之间的显著相似性。

The following results are obtained : Classification of generic singularities in geometric solutions to Monge-Ampere equations. Clarification of Goursat-Legendre correspondence. Basic investigations on singular Legendre submanifolds, in particular singular Legendre curves. Bifurcation of singularities of developables. Estimate on doubly degenerate submanifolds under projective duality. Introduction of the notion of singular coisotropic mappings. Proof of the localization theorem on the symplectic moduli spaces. Basic study on mapping space quotients. Classification theory of singular Legendre knots. Discovery of new singularities of solutions to Monge-Ampere equations in dimension three. Classification of uni-modal curve singularities and determination of their symplectic moduli spaces. Discovery of remarkable similarity between diffeomorphism classification of plane curve singularities and contactomorphism classification of associated Legendre curve singularities.