Nonlinear partial differential equations in differential geometry
About this Title
Robert Hardt, Rice University, Houston, TX and Michael Wolf, Rice University, Houston, TX, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 1996; Volume 2
ISBNs: 978-0-8218-0431-5 (print); 978-1-4704-3901-9 (online)
MathSciNet review: MR1369585
MSC: Primary 58-06; Secondary 00B25, 35-06
What distinguishes differential geometry in the last half of the twentieth century from its earlier history is the use of nonlinear partial differential equations in the study of curved manifolds, submanifolds, mapping problems, and function theory on manifolds, among other topics. The differential equations appear as tools and as objects of study, with analytic and geometric advances fueling each other in the current explosion of progress in this area of geometry in the last twenty years.
This book contains lecture notes of minicourses at the Regional Geometry Institute at Park City, Utah, in July 1992. Presented here are surveys of breaking developments in a number of areas of nonlinear partial differential equations in differential geometry. The authors of the articles are not only excellent expositors, but are also leaders in this field of research. All of the articles provide in-depth treatment of the topics and require few prerequisites and less background than current research articles.
Graduate students and research mathematicians in differential geometry and partial differential equations.
Table of Contents
- A priori estimates and the geometry of the Monge Ampere equation
- The Moser-Trudinger inequality and applications to some problems in conformal geometry
- The effect of curvature on the behavior of harmonic functions and mappings
- Singularities of geometric variational problems
- Proof of the basic regularity theorem for harmonic maps
- Geometric evolution problems