**University Lecture Series**

Volume: 27;
2002;
85 pp;
Softcover

MSC: Primary 53;
Secondary 57; 35

Print ISBN: 978-0-8218-3210-3

Product Code: ULECT/27

List Price: $24.00

Individual Member Price: $19.20

**Electronic ISBN: 978-1-4704-2173-1
Product Code: ULECT/27.E**

List Price: $24.00

Individual Member Price: $19.20

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# Conformal, Riemannian and Lagrangian Geometry: The 2000 Barrett Lectures

Share this page *Editors and Authors: *
*Alexandre Freire; Sun-Yung A. Chang; Paul C. Yang; Karsten Grove; Jon G. Wolfson*

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.

#### Readership

Graduate students and research mathematicians interested in geometry and geometric analysis.

#### Table of Contents

# Table of Contents

## Conformal, Riemannian and Lagrangian Geometry: The 2000 Barrett Lectures

- Cover Cover11 free
- Title v6 free
- Copyright vi7 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. Partial Differential Equations Related to the Gauss-Bonnet-Chern Integrand on 4-manifolds 112 free
- Chapter 2. Geometry of, and via, Symmetries 3142
- Chapter 3. Lagrangian Cycles and Volume 5566
- Back Cover Back Cover197