Geometric Evolution Equations

by CHANG, SHU-CHENG; Chow, Bennett; Chu, Sun-Chin; Lin, Chang-Shou; NATIONAL CENTER FOR THEORETICAL SCIENCES

• ISBN13: 9780821833612
• ISBN10: 0821833618
• Format: Paperback
• Copyright: 2004-10-01
• Publisher: Amer Mathematical Society

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