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Progress in Nonlinear Differential Equations and Their Applications

Geometry of Harmonic Maps

Authors: Xin, Yuanlong

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Softcover $169.00
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About this book

Harmonic maps are solutions to a natural geometrical variational prob­ lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia­ tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em­ phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.

Table of contents (6 chapters)

Buy this book

eBook $129.00
price for USA (gross)
  • ISBN 978-1-4612-4084-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $169.00
price for USA
  • ISBN 978-0-8176-3820-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $169.00
price for USA
  • ISBN 978-1-4612-8644-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Harmonic Maps
Authors
Series Title
Progress in Nonlinear Differential Equations and Their Applications
Series Volume
23
Copyright
1996
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-4084-6
DOI
10.1007/978-1-4612-4084-6
Hardcover ISBN
978-0-8176-3820-7
Softcover ISBN
978-1-4612-8644-8
Series ISSN
1421-1750
Edition Number
1
Number of Pages
X, 246
Topics