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Nonlinear partial differential equations in differential geometry
 
Edited by: Robert Hardt Rice University, Houston, TX
Michael Wolf Rice University, Houston, TX
A co-publication of the AMS and IAS/Park City Mathematics Institute
Front Cover for Nonlinear partial differential equations in differential geometry
Available Formats:
Softcover ISBN: 978-0-8218-0431-5
Product Code: PCMS/2
List Price: $80.00
MAA Member Price: $72.00
AMS Member Price: $64.00
Electronic ISBN: 978-1-4704-3901-9
Product Code: PCMS/2.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $120.00
MAA Member Price: $108.00
AMS Member Price: $96.00
Front Cover for Nonlinear partial differential equations in differential geometry
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  • Front Cover for Nonlinear partial differential equations in differential geometry
  • Back Cover for Nonlinear partial differential equations in differential geometry
Nonlinear partial differential equations in differential geometry
Edited by: Robert Hardt Rice University, Houston, TX
Michael Wolf Rice University, Houston, TX
A co-publication of the AMS and IAS/Park City Mathematics Institute
Available Formats:
Softcover ISBN:  978-0-8218-0431-5
Product Code:  PCMS/2
List Price: $80.00
MAA Member Price: $72.00
AMS Member Price: $64.00
Electronic ISBN:  978-1-4704-3901-9
Product Code:  PCMS/2.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $120.00
MAA Member Price: $108.00
AMS Member Price: $96.00
  • Book Details
     
     
    IAS/Park City Mathematics Series
    Volume: 21996; 339 pp
    MSC: Primary 35; 49; 58; Secondary 53;

    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.

    Readership

    Graduate students and research mathematicians in differential geometry and partial differential equations.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 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
  • Request Review Copy
Volume: 21996; 339 pp
MSC: Primary 35; 49; 58; Secondary 53;

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.

Readership

Graduate students and research mathematicians in differential geometry and partial differential equations.

  • Chapters
  • Introduction
  • 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
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