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Book DetailsContemporary MathematicsVolume: 367; 2005; 235 ppMSC: Primary 53; 35; 57; 58
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.
ReadershipGraduate students and research mathematicians interested in geometric analysis and connections to topology.
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Table of Contents
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Articles
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Sigurd Angenent and Joost Hulshof — Singularities at $t=\infty $ in equivariant harmonic map flow [ MR 2112627 ]
-
Shu-Cheng Chang — Recent developments on the Calabi flow [ MR 2112628 ]
-
Albert Chau — Stability of the Kähler-Ricci flow at complete non-compact Kähler Einstein metrics [ MR 2112629 ]
-
Bennett Chow — A survey of Hamilton’s program for the Ricci flow on 3-manifolds [ MR 2112630 ]
-
Sun-Chin Chu — Basic properties of gradient Ricci solitons [ MR 2112631 ]
-
David Garfinkle and James Isenberg — Numerical studies of the behavior of Ricci flow [ MR 2115754 ]
-
Pengfei Guan and Xi-Nan Ma — Convex solutions of fully nonlinear elliptic equations in classical differential geometry [ MR 2115755 ]
-
Robert Gulliver — Density estimates for minimal surfaces and surfaces flowing by mean curvature [ MR 2115756 ]
-
Dan Knopf — An introduction to the Ricci flow neckpinch [ MR 2115757 ]
-
Lei Ni — Monotonicity and Kähler-Ricci flow [ MR 2115758 ]
-
Miles Simon — Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative [ MR 2115759 ]
-
Luen-Fai Tam — Liouville properties on Kähler manifolds [ MR 2115760 ]
-
Dong-Ho Tsai — Expanding embedded plane curves [ MR 2115761 ]
-
Mu-Tao Wang — Remarks on a class of solutions to the minimal surface system [ MR 2115762 ]
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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.
Graduate students and research mathematicians interested in geometric analysis and connections to topology.
-
Articles
-
Sigurd Angenent and Joost Hulshof — Singularities at $t=\infty $ in equivariant harmonic map flow [ MR 2112627 ]
-
Shu-Cheng Chang — Recent developments on the Calabi flow [ MR 2112628 ]
-
Albert Chau — Stability of the Kähler-Ricci flow at complete non-compact Kähler Einstein metrics [ MR 2112629 ]
-
Bennett Chow — A survey of Hamilton’s program for the Ricci flow on 3-manifolds [ MR 2112630 ]
-
Sun-Chin Chu — Basic properties of gradient Ricci solitons [ MR 2112631 ]
-
David Garfinkle and James Isenberg — Numerical studies of the behavior of Ricci flow [ MR 2115754 ]
-
Pengfei Guan and Xi-Nan Ma — Convex solutions of fully nonlinear elliptic equations in classical differential geometry [ MR 2115755 ]
-
Robert Gulliver — Density estimates for minimal surfaces and surfaces flowing by mean curvature [ MR 2115756 ]
-
Dan Knopf — An introduction to the Ricci flow neckpinch [ MR 2115757 ]
-
Lei Ni — Monotonicity and Kähler-Ricci flow [ MR 2115758 ]
-
Miles Simon — Deforming Lipschitz metrics into smooth metrics while keeping their curvature operator non-negative [ MR 2115759 ]
-
Luen-Fai Tam — Liouville properties on Kähler manifolds [ MR 2115760 ]
-
Dong-Ho Tsai — Expanding embedded plane curves [ MR 2115761 ]
-
Mu-Tao Wang — Remarks on a class of solutions to the minimal surface system [ MR 2115762 ]
