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9780821833612

Geometric Evolution Equations

by ; ; ; ;
  • ISBN13:

    9780821833612

  • ISBN10:

    0821833618

  • Format: Paperback
  • Copyright: 2004-10-01
  • Publisher: Amer Mathematical Society

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Summary

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 Poincare 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), Kahler-Ricci flow, function theory on Kahler 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.

Table of Contents

Preface vii
Photo of Conference Participants viii
Program of the Conference ix
Singularities at t = &infin in equivariant harmonic map flow
1(16)
Sigurd Angenent
Joost Hulshof
Recent developments on the Calabi flow
17(26)
Shu-Cheng Chang
Stability of the Kahler-Ricci flow at complete non-compact Kahler Einstein metrics
43(20)
Albert Chau
A survey of Hamilton's program for the Ricci flow on 3-manifolds
63(16)
Bennett Chow
Basic properties of gradient Ricci solitons
79(24)
Sun-Chin Chu
Numerical studies of the behavior of Ricci flow
103(12)
David Garfinkle
James Isenberg
Convex solutions of fully nonlinear elliptic equations in classical differential geometry
115(14)
Pengfei Guan
Xinan Ma
Density estimates for minimal surfaces and surfaces flowing by mean curvature
129(12)
Robert Gulliver
An introduction to the Ricci flow neckpinch
141(8)
Dan Knopf
Monotonicity and Kahler-Ricci flow
149(18)
Lei Ni
Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative
167(14)
Miles Simon
Liouville properties on Kahler manifolds
181(8)
Luen-Fai Tam
Expanding embedded plane curves
189(40)
Dong-Ho Tsai
Remarks on a class of solutions to the minimal surface system
229
Mu-Tao Wang

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