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

TL;DR

This paper introduces exterior differential systems as a geometric framework for analyzing PDEs, illustrating methods to find suitable geometric settings and applying the Cartan algorithm to study solution moduli spaces.

Contribution

It provides an elementary, geometric approach to PDEs using exterior differential systems, including detailed explanations of the Cartan algorithm and its application to solution classification.

Findings

Demonstrates how to set up geometric frameworks for PDEs

Explains the Cartan algorithm for solution analysis

Applies methods to minimal submanifolds and embedding problems

Abstract

This is an elementary introduction to exterior differential systems motivated by two examples: minimal submanifolds and the isometric embedding problem. The two main goals of the lectures are: 1. To explain how to find an appropriate geometric setting for studying a given system of pde. 2. To explain the Cartan algorithm to determine the moduli space of local solutions to any given exterior differential system and an appropriate initial value problem for the system.