LEADER 04841nam 2200661Ia 450 001 9910782558103321 005 20200520144314.0 010 $a1-281-93808-4 010 $a9786611938086 010 $a981-277-953-1 035 $a(CKB)1000000000557033 035 $a(EBL)1193758 035 $a(SSID)ssj0000288744 035 $a(PQKBManifestationID)12124711 035 $a(PQKBTitleCode)TC0000288744 035 $a(PQKBWorkID)10382940 035 $a(PQKB)10408479 035 $a(MiAaPQ)EBC1193758 035 $a(WSP)00000289 035 $a(Au-PeEL)EBL1193758 035 $a(CaPaEBR)ebr10698964 035 $a(CaONFJC)MIL193808 035 $a(OCoLC)308160132 035 $a(PPN)145857816 035 $a(EXLCZ)991000000000557033 100 $a20081008d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe analysis of harmonic maps and their heat flows$b[electronic resource] /$fFanghua Lin, Changyou Wang 210 $aHackensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (280 p.) 300 $aDescription based upon print version of record. 311 $a981-277-952-3 320 $aIncludes bibliographical references (p. 251-264) and index. 327 $aContents; 3.2 Weakly harmonic maps in dimension two; 3.3 Stationary harmonic maps in higher dimensions; Preface; Organization of the book; Acknowledgements; 1 Introduction to harmonic maps; 1.1 Dirichlet principle of harmonic maps; 1.2 Intrinsic view of harmonic maps; 1.3 Extrinsic view of harmonic maps; 1.4 A few facts about harmonic maps; 1.5 Bochner identity for harmonic maps; 1.6 Second variational formula of harmonic maps; 2 Regularity of minimizing harmonic maps; 2.1 Minimizing harmonic maps in dimension two; 2.2 Minimizing harmonic maps in higher dimensions 327 $a2.3 Federer's dimension reduction principle2.4 Boundary regularity for minimizing harmonic maps; 2.5 Uniqueness of minimizing tangent maps; 2.6 Integrability of Jacobi fields and its applications; 3 Regularity of stationary harmonic maps; 3.1 Weakly harmonic maps into regular balls; 3.4 Stable-stationary harmonic maps into spheres; 4 Blow up analysis of stationary harmonic maps; 4.1 Preliminary analysis; 4.2 Rectifiability of defect measures; 4.3 Strong convergence and interior gradient estimates; 4.4 Boundary gradient estimates; 5 Heat ows to Riemannian manifolds of NPC; 5.1 Motivation 327 $a5.2 Existence of short time smooth solutions5.3 Existence of global smooth solutions under RN < 0; 5.4 An extension of Eells-Sampson's theorem; 6 Bubbling analysis in dimension two; 6.1 Minimal immersion of spheres; 6.2 Almost smooth heat ows in dimension two; 6.3 Finite time singularity in dimension two; 6.4 Bubbling phenomena for 2-D heat ows; 6.5 Approximate harmonic maps in dimension two; 7 Partially smooth heat ows; 7.1 Monotonicity formula and a priori estimates; 7.2 Global smooth solutions and weak compactness; 7.3 Finite time singularity in dimensions at least three 327 $a7.4 Nonuniqueness of heat flow of harmonic maps7.5 Global weak heat flows into spheres; 7.6 Global weak heat flows into general manifolds; 8 Blow up analysis on heat ows; 8.1 Obstruction to strong convergence; 8.2 Basic estimates; 8.3 Stratification of the concentration set; 8.4 Blow up analysis in dimension two; 8.5 Blow up analysis in dimensions n > 3; 9 Dynamics of defect measures in heat flows; 9.1 Generalized varifolds and rectifiability; 9.2 Generalized varifold flows and Brakke's motion; 9.3 Energy quantization of the defect measure; 9.4 Further remarks; Bibliography; Index 330 $aThis book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps from Riemannian surfaces by Helein, as well as on the structure of a singular set of minimizing harmonic maps and stationary harmonic maps by Simon and Lin. The second part of the book contains a systematic coverage of heat flow of harmon 606 $aHarmonic maps$vTextbooks 606 $aHeat equation$vTextbooks 606 $aRiemannian manifolds$vTextbooks 615 0$aHarmonic maps 615 0$aHeat equation 615 0$aRiemannian manifolds 676 $a514/.74 700 $aLin$b Fanghua$065908 701 $aWang$b Changyou$f1967-$01462472 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782558103321 996 $aThe analysis of harmonic maps and their heat flows$93671463 997 $aUNINA