This 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 harmonic maps that includes Eells-Sampson's theorem on global smooth solutions, Struwe's almost regular solutions in dimension two, Sacks-Uhlenbeck's blow-up analysis in dimension two, Chen-Struwe's existence theorem on partially smooth solutions, and blow-up analysis in higher dimensions by Lin and Wang.The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Produkt-Hinweis
Maße
Höhe: 249 mm
Breite: 170 mm
Dicke: 20 mm
Gewicht
ISBN-13
978-981-277-952-6 (9789812779526)
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Schweitzer Klassifikation
Introduction to Harmonic Maps; Regularity Theory of Harmonic Maps; Heat Flow of Harmonic Maps into Manifolds of Non-positive Curvatures; Bubbling Analysis in Dimension Two; Partially Smooth Weak Solutions in High Dimensions; Blow up Analysis of Heat Flow of Harmonic Maps in Higher Dimensions; Rectifiability of Defect Measures and Generalized Varifold Flows.