Harmonic Maps, Conservation Laws and Moving Frames

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Cambridge University Press, Jun 13, 2002 - Mathematics - 264 pages
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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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Contents

Harmonic maps with symmetry
49
Compensations and exotic function spaces
114
Harmonic maps without symmetry
165
Surfaces with mean curvature in L2
221

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Page 257 - R. Hardt, F.-H. Lin: Mappings minimizing the Lp norm of the gradient. Comm. Pure Appl. Math. 40 (1987), 555 588 [Ha85] M.
Page 257 - RS Hamilton, Harmonic maps of manifolds with boundary. Lecture Notes in Math. 471, Springer- Verlag, Berlin 1975.
Page 257 - Hildebrandt, S., and K.-O. Widman, Some regularity results for quasilinear elliptic systems of second order, Math. Z.
Page 255 - R. Coifman, P.-L. Lions. Y. Meyer, S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appi.
Page 257 - L. Nirenberg, On functions of bounded mean oscillations, Comm. Pure Appl. Math. 14 (1961), 415-426.
Page 257 - I. Rodnianski. On the global regularity of wave maps in the critical Sobolev norm, IMRN 13 (2001), 655-677.

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