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Two Reports on Harmonic Maps

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 661/5 ( reviews)

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Book Synopsis Two Reports on Harmonic Maps by : James Eells

Download or read book Two Reports on Harmonic Maps written by James Eells. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and K„hlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.

Two Reports On Harmonic Maps

1995-03-29 Mathematics
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Release : 1995-03-29
Genre : Mathematics
Kind : eBook
Book Rating : 928/5 ( reviews)

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Book Synopsis Two Reports On Harmonic Maps by : James Eells

Download or read book Two Reports On Harmonic Maps written by James Eells. This book was released on 1995-03-29. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.

The Analysis Of Harmonic Maps And Their Heat Flows

2008-05-23 Mathematics
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Release : 2008-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 247/5 ( reviews)

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Book Synopsis The Analysis Of Harmonic Maps And Their Heat Flows by : Fanghua Lin

Download or read book The Analysis Of Harmonic Maps And Their Heat Flows written by Fanghua Lin. This book was released on 2008-05-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry of Harmonic Maps

1996-04-30 Mathematics
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Release : 1996-04-30
Genre : Mathematics
Kind : eBook
Book Rating : 207/5 ( reviews)

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Book Synopsis Geometry of Harmonic Maps by : Yuanlong Xin

Download or read book Geometry of Harmonic Maps written by Yuanlong Xin. This book was released on 1996-04-30. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.

Harmonic Maps

1992 Mathematics
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Release : 1992
Genre : Mathematics
Kind : eBook
Book Rating : 045/5 ( reviews)

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Book Synopsis Harmonic Maps by : James Eells

Download or read book Harmonic Maps written by James Eells. This book was released on 1992. Available in PDF, EPUB and Kindle. Book excerpt: These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.

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