000			04709nam a22003978i 4500
001			CR9780511543036
003			UkCbUP
005			20200124160241.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090505s2002||||enk o ||1 0|eng|d
020			_a9780511543036 (ebook)
020			_z9780521811606 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
041	1		_aeng _hfre
050	0	0	_aQA614.73 _b.H45 2002
082	0	0	_a514/.74 _221
100	1		_aHélein, Frédéric, _d1963- _eauthor.
245	1	0	_aHarmonic maps, conservation laws, and moving frames / _cFrédéric Hélein.
246	3		_aHarmonic Maps, Conservation Laws & Moving Frames
250			_aSecond edition.
264		1	_aCambridge : _bCambridge University Press, _c2002.
300			_a1 online resource (xxv, 264 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v150
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_g1 _tGeometric and analytic setting _g1 -- _g1.1 _tThe Laplacian on (M, g) _g2 -- _g1.2 _tHarmonic maps between two Riemannian manifolds _g5 -- _g1.3 _tConservation laws for harmonic maps _g11 -- _g1.3.1 _tSymmetries on N _g12 -- _g1.3.2 _tSymmetries on M: the stress-energy tensor _g18 -- _g1.3.3 _tConsequences of theorem 1.3.6 _g24 -- _g1.4 _tVariational approach: Sobolev spaces _g31 -- _g1.4.1 _tWeakly harmonic maps _g37 -- _g1.4.2 _tWeakly Noether harmonic maps _g42 -- _g1.4.3 _tMinimizing maps _g42 -- _g1.4.4 _tWeakly stationary maps _g43 -- _g1.4.5 _tRelation between these different definitions _g43 -- _g1.5 _tRegularity of weak solutions _g46 -- _g2 _tHarmonic maps with symmetry _g49 -- _g2.1 _tBacklund transformation _g50 -- _g2.1.1 _tS[superscript 2]-valued maps _g50 -- _g2.1.2 _tMaps taking values in a sphere S[superscript n], n [greater than or equal] 2 _g54 -- _g2.1.3 _tComparison _g56 -- _g2.2 _tHarmonic maps with values into Lie groups _g58 -- _g2.2.1 _tFamilies of curvature-free connections _g65 -- _g2.2.2 _tThe dressing _g72 -- _g2.2.3 _tUhlenbeck factorization for maps with values in U(n) _g77 -- _g2.2.4 _tS[superscript 1]-action _g79 -- _g2.3 _tHarmonic maps with values into homogeneous spaces _g82 -- _g2.4 _tSynthesis: relation between the different formulations _g95 -- _g2.5 _tCompactness of weak solutions in the weak topology _g101 -- _g2.6 _tRegularity of weak solutions _g109 -- _g3 _tCompensations and exotic function spaces _g114 -- _g3.1 _tWente's inequality _g115 -- _g3.1.1 _tThe inequality on a plane domain _g115 -- _g3.1.2 _tThe inequality on a Riemann surface _g119 -- _g3.2 _tHardy spaces _g128 -- _g3.3 _tLorentz spaces _g135 -- _g3.4 _tBack to Wente's inequality _g145 -- _g3.5 _tWeakly stationary maps with values into a sphere _g150 -- _g4 _tHarmonic maps without symmetry _g165 -- _g4.1 _tRegularity of weakly harmonic maps of surfaces _g166 -- _g4.2 _tGeneralizations in dimension 2 _g187 -- _g4.3 _tRegularity results in arbitrary dimension _g193 -- _g4.4 _tConservation laws for harmonic maps without symmetry _g205 -- _g4.4.1 _tConservation laws _g206 -- _g4.4.2 _tIsometric embedding of vector-bundle-valued differential forms _g211 -- _g4.4.3 _tA variational formulation for the case m = n = 2 and p = 1 _g215 -- _g4.4.4 _tHidden symmetries for harmonic maps on surfaces? _g218 -- _g5 _tSurfaces with mean curvature in L[superscript 2] _g221 -- _g5.1 _tLocal results _g224 -- _g5.2 _tGlobal results _g237 -- _g5.3 _tWillmore surfaces _g242 -- _g5.4 _tEpilogue: Coulomb frames and conformal coordinates _g244.
520			_aThe 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.
650		0	_aHarmonic maps.
650		0	_aRiemannian manifolds.
776	0	8	_iPrint version: _z9780521811606
830		0	_aCambridge tracts in mathematics ; _v150.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511543036
999			_c518583 _d518581