04841nam 2200661Ia 450 991078255810332120200520144314.01-281-93808-49786611938086981-277-953-1(CKB)1000000000557033(EBL)1193758(SSID)ssj0000288744(PQKBManifestationID)12124711(PQKBTitleCode)TC0000288744(PQKBWorkID)10382940(PQKB)10408479(MiAaPQ)EBC1193758(WSP)00000289 (Au-PeEL)EBL1193758(CaPaEBR)ebr10698964(CaONFJC)MIL193808(OCoLC)308160132(PPN)145857816(EXLCZ)99100000000055703320081008d2008 uy 0engur|n|---|||||txtccrThe analysis of harmonic maps and their heat flows[electronic resource] /Fanghua Lin, Changyou WangHackensack, NJ World Scientificc20081 online resource (280 p.)Description based upon print version of record.981-277-952-3 Includes bibliographical references (p. 251-264) and index.Contents; 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 dimensions2.3 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 Motivation5.2 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 three7.4 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; IndexThis 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 harmonHarmonic mapsTextbooksHeat equationTextbooksRiemannian manifoldsTextbooksHarmonic mapsHeat equationRiemannian manifolds514/.74Lin Fanghua65908Wang Changyou1967-1462472MiAaPQMiAaPQMiAaPQBOOK9910782558103321The analysis of harmonic maps and their heat flows3671463UNINA