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.
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Editorial Reviews
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"...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
"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
Book Description
The author 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. It introduces the necessary mathematical tools for the study of harmonic maps and presents applications of the methods and theory, bringing in results from recent research on the regularity of weak solutions. The book will be of particular interest to graduate students and researchers in geometry, analysis and partial differential equations. It will also have a wide appeal within the mathematical physics community.
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Inside This Book
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First Sentence:
This chapter essentially describes the objects and properties that will interest us in this work. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
weakly harmonic map, conformal immersion, dressing action, harmonic maps, image manifold, loop group Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter essentially describes the objects and properties that will interest us in this work. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
weakly harmonic map, conformal immersion, dressing action, harmonic maps, image manifold, loop group Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
books:
- Seminar on Nonlinear Partial Differential Equations (Mathematical Sciences Research Institute Publications) by S.S. Chern in Back Matter
- Partial Differential Equations (Lecture Notes in Mathematics) by S. S. Chern in Back Matter
- Nonblocking Electronic and Photonic Switching Fabrics (Grundlehren der Mathematischen Wissenschaften (Springer)) in Back Matter
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