from International Press

Advanced Lectures in Mathematics, Vol. 14

Handbook of Geometric Analysis, No. 3

Edited by
Lizhen Ji (University of Michigan)
Peter Li (University of California, Irvine)
Richard Schoen (Stanford University)
Leon Simon (Stanford University)

Publication Details

Softcover. 472 pages. 4 pages of color photographs.
ISBN: 978-1-57146-205-3
Published: August 2010
Publisher: International Press of Boston
List price: $65.00. Discounts may apply.

Full Description

Geometric Analysis combines differential equations and differential geometry. An important aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Ampère equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications.

This handbook of geometric analysis - the third to be published in the ALM series - provides introductions to and surveys of important topics in geometric analysis and their applications to related fields. It can be used as a reference by graduate students and researchers.

Table of Contents

• A Survey of Einstein Metrics on 4-manifolds
  Michael T. Anderson
• Sphere Theorems in Geometry
  Simon Brendle and Richard Schoen
• Curvature Flows and CMC Hypersurfaces
  Claus Gerhardt
• Geometric Structures on Riemannian Manifolds
  Naichung Conan Leung
• Symplectic Calabi-Yau Surfaces
  Tian-Jun Li
• Lectures on Stability and Constant Scalar Curvature
  D.H. Phong and Jacob Sturm
• Analytic Aspect of Hamilton's Ricci Flow
  Xi-Ping Zhu

About the Series

Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cutting-edge results.

Other volumes in the Advanced Lectures in Mathematics series

Vol. 13. Handbook of Geometric Analysis, No. 2

Vol. 12. Cohomology of Groups and Algebraic K-theory

Vol. 11. Recent Advances in Geometric Analysis

Vol. 10. Trends in Partial Differential Equations

Vol. 9. Automorphic Forms and the Langlands Program

Vol. 8. Recent Developments in Algebra and Related Areas

Vol. 7. Handbook of Geometric Analysis, No. 1

Vol. 6. Geometry, Analysis and Topology of Discrete Groups

Vol. 5. Fourth International Congress of Chinese Mathematicians (2007)

Vol. 4. Variational Principles for Discrete Surfaces

Vol. 3. Computational Conformal Geometry

Vol. 2. Asymptotic Theory in Probability and Statistics with Applications

Vol. 1. Superstring Theory

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