Harmonic Maps, Conservation Laws and Moving Frames

2. Auflage 2013
ISBN: 978-0-521-81160-6
Verlag: Cambridge University Press

Buch, Englisch, Band 150, 292 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 577 g

Reihe: 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.

Autoren/Hrsg.

Hélein, Frédéric

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie Analytische Topologie

Inhaltsverzeichnis

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.