© 2013

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

  • Presents the recent crucial developments of harmonic maps into biharmonic maps, of wave maps into biwave maps and of Yang-Mills fields into bi-Yang-Mills fields

  • Discusses exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields

  • Introduces biwave maps (generalizing wave maps) and bi-Yang-Mills fields (generalizing Yang-Mills fields)


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

  1. 1., Department of MathematicsUniversity of Mary WashingtonFredericksburgUSA

Bibliographic information


From the book reviews:

“The monograph under review gathers developments in the theory of harmonic maps, wave maps, and Yang-Mills fields, and their generalisations to biharmonic maps, biwave maps, and bi-Yang-Mills fields. … The present book is a very useful text for experts in the field of harmonic and biharmonic maps, providing us with a rich and updated source of information on the subject.” (Monica Alice Aprodu, Mathematical Reviews, July, 2014)