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The Curve Shortening Problem

The Curve Shortening Problem by Kai-Seng Chou
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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
CRC Press; March 2001
266 pages; ISBN 9781420035704
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Title: The Curve Shortening Problem
Author: Kai-Seng Chou; Xi-Ping Zhu
 
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