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Geometric Evolution Equations
Edited by: Shu-Cheng Chang, National Tsing Hua University, Hsinchu, Taiwan, Bennett Chow, University of California San Diego, La Jolla, CA, and Sun-Chin Chu and Chang-Shou Lin, National Chung Cheng University, Chia-Yi, Taiwan
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Contemporary Mathematics
2005; 235 pp; softcover
Volume: 367
ISBN-10: 0-8218-3361-8
ISBN-13: 978-0-8218-3361-2
List Price: US$76
Member Price: US$60.80
Order Code: CONM/367
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The Workshop on Geometric Evolution Equations was a gathering of experts that produced this comprehensive collection of articles. Many of the papers relate to the Ricci flow and Hamilton's program for understanding the geometry and topology of 3-manifolds.

The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solution of Thurston's Geometrization Conjecture and the Poincaré Conjecture. Yet applying the method poses serious technical problems. Contributors to this volume explain some of these issues and demonstrate a noteworthy deftness in the handling of technical areas.

Various topics in geometric evolution equations and related fields are presented. Among other topics covered are minimal surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kähler-Ricci flow, function theory on Kähler manifolds, flows of plane curves, convexity estimates, and the Christoffel-Minkowski problem.

The material is suitable for graduate students and researchers interested in geometric analysis and connections to topology.

Related titles of interest include The Ricci Flow: An Introduction.

Readership

Graduate students and research mathematicians interested in geometric analysis and connections to topology.

Table of Contents

  • S. Angenent and J. Hulshof -- Singularities at \(t=\infty\) in equivariant harmonic map flow
  • S.-C. Chang -- Recent developments on the Calabi flow
  • A. Chau -- Stability of the Kähler-Ricci flow at complete non-compact Kähler Einstein metrics
  • B. Chow -- A survey of Hamilton's program for the Ricci flow on 3-manifolds
  • S.-C. Chu -- Basic properties of gradient Ricci solitons
  • D. Garfinkle and J. Isenberg -- Numerical studies of the behavior of Ricci flow
  • P. Guan and X.-N. Ma -- Convex solutions of fully nonlinear elliptic equations in classical differential geometry
  • R. Gulliver -- Density estimates for minimal surfaces and surfaces flowing by mean curvature
  • D. Knopf -- An introduction to the Ricci flow neckpinch
  • L. Ni -- Monotonicity and Kähler-Ricci flow
  • M. Simon -- Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative
  • L.-F. Tam -- Liouville properties on Kähler manifolds
  • D.-H. Tsai -- Expanding embedded plane curves
  • M.-T. Wang -- Remarks on a class of solutions to the minimal surface system
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