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  1. Home
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  3. Harmonic Maps, Conservation Laws and Moving Frames
  • Cited by 175
Publisher:
Cambridge University Press
Online publication date:
August 2009
Print publication year:
2002
Online ISBN:
9780511543036
DOI:
https://doi.org/10.1017/CBO9780511543036
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (150)
Information

Book description

The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a 'Coulomb moving frame' is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.

Reviews

'The book is very well written and it contains truly beautiful geometrical analysis. It also contains a quick, direct introduction to the current research.’

Source: EMS Newsletter

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