Harmonic Maps, Conservation Laws and Moving Frames

ISBN-13: 9780521811606 / Angielski / Twarda / 2002 / 292 str.

Frederic Helein; B. Bollobas; W. Fulton

Opis

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.

Recenzje

'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

Spis treści

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.