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THE ANALYSIS OF HARMONIC MAPS AND THEIR HEAT FLOWS
by Fanghua Lin (New York University, USA) & Changyou Wang (University of Kentucky, USA)
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.
Contents:
- Introduction to Harmonic Maps
- Regularity of Minimizing Harmonic
Maps
- Regularity of Stationary Harmonic Maps
- Blow up Analysis of Stationary Harmonic Maps
- Heat Flows to Riemannian Manifolds of NPC
- Bubbling Analysis in Dimension Two
- Partially Smooth Heat Flows
- Blow up Analysis on Heat Flow
- Dynamics of Defect Measures in Heat Flows
Readership: Graduate students and researchers in geometric partial
differential equations and geometric analysis.
| 280pp |
Pub. date: May 2008 |
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