Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

  • Yuan-Jen Chiang

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Yuan-Jen Chiang
    Pages 1-83
  3. Yuan-Jen Chiang
    Pages 85-162
  4. Yuan-Jen Chiang
    Pages 163-242
  5. Yuan-Jen Chiang
    Pages 243-304
  6. Yuan-Jen Chiang
    Pages 305-338
  7. Yuan-Jen Chiang
    Pages 339-350
  8. Yuan-Jen Chiang
    Pages 351-357
  9. Yuan-Jen Chiang
    Pages 359-370
  10. Yuan-Jen Chiang
    Pages 371-378
  11. Back Matter
    Pages 379-399

About this book


Harmonic maps between Riemannian manifolds were first established in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.


Yang-Mills fields bi-Yang-Mills fields biharmonic maps biwave maps harmonic maps wave maps

Authors and affiliations

  • Yuan-Jen Chiang
    • 1
  1. 1., Department of MathematicsUniversity of Mary WashingtonFredericksburgUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Basel 2013
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0533-9
  • Online ISBN 978-3-0348-0534-6
  • Series Print ISSN 1660-8046
  • Series Online ISSN 1660-8054
  • Buy this book on publisher's site