IAS/Park City Mathematics Series 1996; 339 pp; softcover Volume: 2 ISBN10: 0821804316 ISBN13: 9780821804315 List Price: US$75 Member Price: US$60 Order Code: PCMS/2
 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 indepth treatment of the topics and require few prerequisites and less background than current research articles. Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price. Readership Graduate students and research mathematicians in differential geometry and partial differential equations. Table of Contents  R. M. Hardt and M. Wolf  Introduction
 L. A. Caffarelli  A priori estimates and the geometry of the Monge Ampere equation
 S.Y. A. Chang  The MoserTrudinger inequality and applications to some problems in conformal geometry
 R. M. Schoen  The effect of curvature on the behavior of harmonic functions and mappings
 L. M. Simon  Singularities of geometric variational problems
 L. M. Simon  Proof of the basic regularity theorem for harmonic maps
 M. Struwe  Geometric evolution problems
