from International Press

Advanced Lectures in Mathematics, Vol. 13

Handbook of Geometric Analysis, No. 2

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

Publication Details

Softcover. 431 pages. 4 pages of color photographs.
ISBN: 978-1-57146-204-6
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 second 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

• Heat Kernels on Metric Measure Spaces with Regular Volume Growth
  Alexander Grigor'yan
• A Convexity Theorem and Reduced Delzant Spaces
  Bong H. Lian and Bailin Song
• Localization and some Recent Applications
  Bong H. Lian and Kefeng Liu
• Gromov-Witten Invariants of Toric Calabi-Yau Threefolds
  Chiu-Chu Melissa Liu
• Survey on Affine Spheres
  John Loftin
• Convergence and Collapsing Theorems in Riemannian Geometry
  Xiaochun Rong
• Geometric Transformations and Soliton Equations
  Chuu-Lian Terng
• Affine Integral Geometry from a Differentiable Viewpoint
  Deane Yang
• Classification of Fake Projective Planes
  Sai-Kee Yeung

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. 14. Handbook of Geometric Analysis, No. 3

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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