Overview

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.

Full Product Details

Author:   Fanghua Lin (New York Univ, Usa) ,  Changyou Wang (Univ Of Kentucky, Usa)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Dimensions:   Width: 17.00cm , Height: 2.00cm , Length: 24.90cm
Weight:   0.612kg
ISBN:  

9789812779526

ISBN 10:   9812779523
Pages:   280
Publication Date:   26 May 2008
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

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