Harmonic Maps, Conservation Laws and Moving Frames
Edition: 2 edition
Publisher: Cambridge University Press
Published: June 15, 2002
Language: eng; fre
Format: Hardcover
Number of pages: 288
ISBN-13: 9780521811606
Subjects: Analytic topology; Calculus & mathematical analysis; Geometry; Topology - General; Harmonic Analysis; Mathematics; Science/Mathematics; Probability & Statistics - General; Mathematics / Differential Equations; Harmonic maps; Riemannian Manifolds
First sentence: This chapter essentially describes the objects and properties that will interest us in this work.
Description: 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.