Overview

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.

Full Product Details

Author:   Shu-Cheng Chang ,  Bennett Chow ,  Sun-Chin Chu ,  Chang-Shou Lin
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Edition:   illustrated edition
Volume:   No. 367
Weight:   0.449kg
ISBN:  

9780821833612

ISBN 10:   0821833618
Pages:   235
Publication Date:   30 January 2005
Recommended Age:   From 8 To 12
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Temporarily unavailable  
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Table of Contents

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

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