Conformal, Riemannian and Lagrangian Geometry ：The 2000 Barrett Lectures ( University Lecture Series )

Publication subTitle ：The 2000 Barrett Lectures

Publication series ：University Lecture Series

Author： Sun-Yung A. Chang;Paul C. Yang;Karsten Grove  

Publisher： American Mathematical Society‎

Publication year： 2002

E-ISBN: 9781470421731

P-ISBN(Paperback): 9780821832103

Subject： O185 projective (projection) Geometry, geometry

Keyword： Geometry and Topology

Language： ENG

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Conformal, Riemannian and Lagrangian Geometry

Description

Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus of variations. The lectures provide an up-do-date overview and an introduction to the research literature in each of their areas. This very readable introduction should prove useful to graduate students and researchers in differential geometry and geometric analysis.

Chapter

Cover

Title

Copyright

Contents

Preface

Chapter 1. Partial Differential Equations Related to the Gauss-Bonnet-Chern Integrand on 4-manifolds

Introduction

1. Finiteness of conformally flat structures

2. Background on a σ[sub(2)]

3. Deforming σ[sub(2)] to a positive function

4. Deforming σ[sub(2)] to a constant

Bibliography

Chapter 2. Geometry of, and via, Symmetries

Introduction

1. Geometry of isometry groups

2. Structure and classification program

3. Constructions and examples

4. Emergence of isometries

5. Open problems

Bibliography

Chapter 3. Lagrangian Cycles and Volume

Introduction

1. The variational problem

2. Existence

3. Regularity: cones and monotonicity

Bibliography

Back Cover

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