The Curve Shortening Problem

ISBN: 9780367397531 出版年：2001 页码：266 Chou, Kai-Seng Zhu, Xi-Ping CRC Press

BASIC RESULTS Short Time Existence Facts from Parabolic Theory Evolution of Geometric Quantities INVARIANT SOLUTIONS FOR THE CURVE SHORTENING FLOW Travelling Waves Spirals The Support Function of a Convex Curve Self-Similar Solutions THE CURVATURE-EIKONAL FLOW FOR CONVEX CURVES Blaschke Selection Theorem Preserving Convexity and Shrinking to a Point Gage-Hamilton Theorem The Contracting Case of the ACEF The Stationary case of the ACEF The Expanding Case of the ACEF THE CONVEX GENERALIZED CURVE SHORTENING FLOW Results from Brunn-Minkowski Theory The AGCSF for s in (1/3,1) The Affine Curve Shortening Flow Uniqueness of Self-Similar Solutions THE NON-CONVEX CURVE SHORTENING FLOW An Isoperimetric Ratio Limits of the Rescaled Flow Classification of Singularities A CLASS OF NON-CONVEX ANISOTROPIC FLOWS Decrease in Total Absolute Curvature Existence of a Limit Curve Shrinking to a Point A Whisker Lemma The Convexity Theorem EMBEDDED CLOSED GEODESICS ON SURFACES Basic Results The Limit Curve Shrinking to a Point Convergence to a Geodesic THE NON-CONVEX GENERALIZED CURVE SHORTENING FLOW Short Time Existence The Number of Convex Arcs The Limit Curve Removal of Interior Singularities The Almost Convexity Theorem BIBLIOGRAPHY