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

1. Front Matter

   Pages i-xxi

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2. Harmonic Maps

   • Yuan-Jen Chiang

   Pages 1-83

3. Wave Maps

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   Pages 85-162

4. Yang-Mills Fields

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   Pages 163-242

5. Biharmonic Maps

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   Pages 243-304

6. Biwave Maps

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   Pages 305-338

7. Bi-Yang-Mills Fields

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   Pages 339-350

8. Exponentially Harmonic Maps

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   Pages 351-357

9. Exponential Wave Maps

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   Pages 359-370

10. Exponential Yang-Mills Connections

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    Pages 371-378

11. Back Matter

    Pages 379-399

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Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson 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 by Guoying Jiang 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 by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa 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
• partial differential equations

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)

• , Department of Mathematics, University of Mary Washington, Fredericksburg, USA

  Yuan-Jen Chiang

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