Biharmonic Maps
 YuanJen Chiang
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Abstract
The last five decades have witnessed many developments in the theory of harmonic maps. To become acquainted to some of these, the reader is referred to two reports and a survey paper by Eells and Lemaire [119, 122, 124] about the developments of harmonic maps up to 1988 for details. Several books on harmonic maps [203, 205, 206, 389, 425] are also available. In this chapter, we follow the notions and notations of harmonic maps between Riemannian manifolds by Eells Sampson [129] in the introduction.We discuss the crucial topics in harmonic maps including fundamentals, regularity, maps of surfaces, maps of KRahler manifolds, maps into groups and Grassmannians, harmonic maps, loop groups, and integrable systems, harmonicmorphisms, maps of singular spaces, and transversally harmonic maps. Since the theory of harmonic maps has been developed over half a century, it is impossible to provide full details. However, we try to present the most important components of the topics.
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 Title
 Biharmonic Maps
 Book Title
 Developments of Harmonic Maps, Wave Maps and YangMills Fields into Biharmonic Maps, Biwave Maps and BiYangMills Fields
 Pages
 pp 243304
 Copyright
 2013
 DOI
 10.1007/9783034805346_4
 Print ISBN
 9783034805339
 Online ISBN
 9783034805346
 Series Title
 Frontiers in Mathematics
 Series ISSN
 16608046
 Publisher
 Springer Basel
 Copyright Holder
 Springer Basel
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 Authors

 YuanJen Chiang ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of Mary Washington, Fredericksburg, VA, USA
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