Nonlinear Partial Differential Equations in Differential Geometry / Edition 1

Nonlinear Partial Differential Equations in Differential Geometry / Edition 1

by Robert Hardt
     
 

ISBN-10: 0821804316

ISBN-13: 9780821804315

Pub. Date: 12/05/1995

Publisher: American Mathematical Society

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

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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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Product Details

ISBN-13:
9780821804315
Publisher:
American Mathematical Society
Publication date:
12/05/1995
Series:
IAS Park City Mathematics Series, #2
Pages:
339
Product dimensions:
6.90(w) x 9.90(h) x 0.80(d)

Table of Contents

Preface
Introduction1
A Priori Estimates and the Geometry of the Monge-Ampere Equation5
The Moser-Trudinger Inequality and Applications to Some Problems in Conformal Geometry65
The Effect of Curvature on the Behavior of Harmonic Functions and Mappings127
Singularities of Geometric Variational Problems185
Proof of the Basic Regularity Theorem for Harmonic Maps225
Geometric Evolution Problems257

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