Harmonic Maps, Conservation Laws and Moving Frames

Frédéric Hélein (Ecole Normale Supérieure, Lyon)

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Hardback

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English

Cambridge University Press
22 October 2002

Calculus & mathematical analysis; Geometry; Analytic topology

Series: Cambridge Tracts in Mathematics

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.

By: Frédéric Hélein (Ecole Normale Supérieure Lyon)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Volume: 150
Dimensions: Height: 231mm, Width: 155mm, Spine: 20mm
Weight: 627g
ISBN: 9780521811606
ISBN 10: 0521811600
Series: Cambridge Tracts in Mathematics
Pages: 292
Publication Date: 22 October 2002
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Reviews for Harmonic Maps, Conservation Laws and Moving Frames

'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