Harmonic Maps, Conservation Laws and Moving Frames

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Harmonic Maps, Conservation Laws and...

Harmonic Maps, Conservation Laws and Moving Frames

Name: Harmonic Maps, Conservation Laws and Moving Frames
ISBN: 9780511016608

Frédéric Hélein

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This accessible introduction to harmonic map theory and its analytical aspects, covers 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. It then presents 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 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.

類別:

Mathematics - Analysis

年:

2002

版本:

2nd edition

語言:

english

頁數:

290

ISBN 10:

0511016603