Harmonic Maps, Conservation Laws and Moving Frames / Edition 2

by Frédéric Hélein

Overview

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.

Product Details

ISBN-13:	9780521811606
Publisher:	Cambridge University Press
Publication date:	06/13/2002
Series:	Cambridge Tracts in Mathematics , #150
Edition description:	Revised Edition
Pages:	292
Product dimensions:	6.10(w) x 9.09(h) x 0.79(d)

Table of Contents

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.

Editorial Reviews

"...an excellent overview...The reviewer has really enjoyed reading this book." MATH

"The presentation of the material is excellent. The book is as self-contained as it can be....The concepts that are introduced are very carefully motivated. Because the book also gives an overview about recent research results (even updated for the second edition), it is not only a pleasure to read, but also a very good reference book for research." Mathematical Reviews

From the Publisher

This book provides 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 and stressing the interplay between geometry, the role of symmetrics, and weak solutions. The theory of completely integrable systems for harmonic maps is explained, and two chapters are devoted to recent results on the regularity of weak solutions. Hélein is affiliated with Ecole Normale Supérieure de Cachan. The first edition of the book was published in French as Applications harmoniques, lois de conservation et repeéres mobiles, Diderot Editeur, 1996. An English version, translated by L. Almeida, was published by Diderot Editeur in 1997. Annotation c. Book News, Inc., Portland, OR