Geometric evolution equations : National Center for Theoretical Sciences Workshop on Geometric Evolution Equations, National Tsing Hua University, Hsinchu, Taiwan, July 15-August 14, 2002
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Bibliographic Information
Geometric evolution equations : National Center for Theoretical Sciences Workshop on Geometric Evolution Equations, National Tsing Hua University, Hsinchu, Taiwan, July 15-August 14, 2002
（Contemporary mathematics, v. 367）
American Mathematical Society, c2005
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC22:515.353/C3622080022496
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Includes bibliographical references
Description and Table of Contents
Description
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
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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