Nonlinear Partial Differential Equations in Differential Geometry / Edition 1

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Brand new. We distribute directly for the publisher. 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. Read more Show Less

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Overview

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.

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Editorial Reviews

Booknews
The lecture notes from a July 1992 minicourse in Park City, Utah, for graduate students and research mathematicians in differential geometry and partial differential equations. They survey the current state of such aspects as the Moser-Trudinger inequality and its applications to some problems in conformal geometry, the effect of curvature on the behavior of harmonic functions and mapping, and singularities of geometric variational problems. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821804315
  • Publisher: American Mathematical Society
  • Publication date: 12/5/1995
  • Series: IAS Park City Mathematics Series , #2
  • Edition number: 1
  • Pages: 339
  • Product dimensions: 6.90 (w) x 9.90 (h) x 0.80 (d)

Table of Contents

Preface
Introduction 1
A Priori Estimates and the Geometry of the Monge-Ampere Equation 5
The Moser-Trudinger Inequality and Applications to Some Problems in Conformal Geometry 65
The Effect of Curvature on the Behavior of Harmonic Functions and Mappings 127
Singularities of Geometric Variational Problems 185
Proof of the Basic Regularity Theorem for Harmonic Maps 225
Geometric Evolution Problems 257
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