A01=Kai-Seng Chou
A01=Xi-Ping Zhu
Admissible Triple
anisotropic curve evolution
arc
Ascoli Arzela Theorem
Author_Kai-Seng Chou
Author_Xi-Ping Zhu
Category=PBF
Category=PBKJ
Category=PBMP
Category=PBW
cauchy
Cauchy Problem
Closed Curve
Closed Geodesics
Convex Bodies
Convex Curve
convexity theorem
Counterclockwise
Curve Shortening
differential geometry
Ection Point
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Follow
General Ow
geometric flow applications
geometric flows
Grim Reaper
Initial Curve
Isoperimetric Inequality
length
Limit Curve
Lipschitz Continuous Map
mathematical analysis
maximum
Nice Arc
Parabolic Boundary
parameter
principle
self-similar
Self-similar Solutions
simple closed geodesics
solution
strong
Strong Maximum Principle
support
Support Function
Tangent Angle
Total Curvature
Uniformly Convex
Product details
- ISBN 9781584882138
- Weight: 440g
- Dimensions: 156 x 234mm
- Publication Date: 06 Mar 2001
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results.
The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson's convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem.
Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.
Chou, Kai-Seng; Zhu, Xi-Ping
