New from International Press, August 2008

Advanced Lectures in Mathematics, Vol. 7

Handbook of Geometric Analysis, No. 1

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

This handbook of geometric analysis—the first of the two to be published in the ALM series—presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas.

Publication Details

Hardcover. 676 pages.
ISBN-13: 978-1-57146-130-8
ISBN-10: 1-57146-130-2
2000 MSC: 01-02
Published: August 2008
Publisher: International Press of Boston
List price: $97.00

Full Description

Geometric Analysis combines differential equations with differential geometry. An important aspect of geometric analysis is to approach 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-Amperè 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 first of the two to be published in the ALM series—presents introductions and survey papers treating important topics in geometric analysis, with their applications to related fields. It can be used as a reference by graduate students and by researchers in related areas.

Table of Contents

• Numerical Approximations to Extremal Metrics on Toric Surfaces
  (R. S. Bunch, Simon K. Donaldson)
• Kähler Geometry on Toric Manifolds, and some other Manifolds with Large Symmetry
  (Simon K. Donaldson)
• Gluing Constructions of Special Lagrangian Cones
  (Mark Haskins, Nikolaos Kapouleas)
• Harmonic Mappings
  (Jürgen Jost)
• Harmonic Functions on Complete Riemannian Manifolds
  (Peter Li)
• Complexity of Solutions of Partial Differential Equations
  (Fang Hua Lin)
• Variational Principles on Triangulated Surfaces
  (Feng Luo)
• Asymptotic Structures in the Geometry of Stability and Extremal Metrics
  (Toshiki Mabuchi)
• Stable Constant Mean Curvature Surfaces
  (William H. Meeks III, Joaquín Pérez, Antonio Ros)
• A General Asymptotic Decay Lemma for Elliptic Problems
  (Leon Simon)
• Uniformization of Open Nonnegatively Curved Kähler Manifolds in Higher Dimensions
  (Luen-Fai Tam)
• Geometry of Measures: Harmonic Analysis Meets Geometric Measure Theory
  (Tatiana Toro)
• Lectures on Mean Curvature Flows in Higher Codimensions
  (Mu-Tao Wang)
• Local and Global Analysis of Eigenfunctions on Riemannian Manifolds
  (Steve Zelditch)
• Yau’s Form of Schwarz Lemma and Arakelov Inequality On Moduli Spaces of Projective Manifolds
  (Kang Zuo)

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. 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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