**Contemporary Mathematics**

Volume: 367;
2005;
235 pp;
Softcover

MSC: Primary 53; 35; 57; 58;

Print ISBN: 978-0-8218-3361-2

Product Code: CONM/367

List Price: $80.00

Individual Member Price: $64.00

**Electronic ISBN: 978-0-8218-7957-3
Product Code: CONM/367.E**

List Price: $80.00

Individual Member Price: $64.00

# Geometric Evolution Equations

Share this page *Edited by *
*Shu-Cheng Chang; Bennett Chow; Sun-Chin Chu; Chang-Shou Lin*

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

## Geometric Evolution Equations

- Contents v6 free
- Preface vii8 free
- Photo of Conference Participants viii9 free
- Program of the Conference ix10 free
- Singularities at t = ∞ in equivariant harmonic map flow 112 free
- Recent developments on the Calabi flow 1728
- Stability of the Kähler-Ricci flow at complete non-compact Kähler Einstein metrics 4354
- A survey of Hamilton's program for the Ricci flow on 3-manifolds 6374
- Basic properties of gradient Ricci solitons 7990
- Numerical studies of the behavior of Ricci flow 103114
- Convex solutions of fully nonlinear elliptic equations in classical differential geometry 115126
- Density estimates for minimal surfaces and surfaces flowing by mean curvature 129140
- An introduction to the Ricci flow neckpinch 141152
- Monotonicity and Kähler-Ricci flow 149160
- Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative 167178
- Liouville properties on Kähler manifolds 181192
- Expanding embedded plane curves 189200
- Remarks on a class of solutions to the minimal surface system 229240