Exterior differential systems: a geometric approach to PDE. Lecture notes from the 1997 Daewoo workshop

摘要

This is an elementary introduction to exterior differential systems motivatedby two examples: minimal submanifolds and the isometric embedding problem. Thetwo main goals of the lectures are: 1. To explain how to find an appropriategeometric setting for studying a given system of pde. 2. To explain the Cartanalgorithm to determine the moduli space of local solutions to any givenexterior differential system and an appropriate initial value problem for thesystem.