Harmonic Maps, Conservation Laws and Moving Frames

Accessible and pedagogical introduction to the theory of harmonic maps, covering recent results and applications.

Frédéric Hélein (Author)

9780521811606, Cambridge University Press

Hardback, published 13 June 2002

292 pages
23.1 x 15.5 x 2 cm, 0.627 kg

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

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.

Preface
Introduction
Acknowledgements
Notations
1. Geometric and analytic setting
2. Harmonic maps with symmetries
3. Compensations and exotic function spaces
4. Harmonic maps without symmetries
5. Surfaces with mean curvature in L2
References.

Subject Areas: Topology [PBP], Geometry [PBM], Calculus & mathematical analysis [PBK]