| The Curve Shortening Problem Contributor(s): Chou, Kai-Seng (Author), Zhu, XI-Ping (Author) |
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ISBN: 1584882131 ISBN-13: 9781584882138 Publisher: CRC Press OUR PRICE: $190.00 Product Type: Hardcover Published: March 2001 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Technology & Engineering | Engineering (general) - Mathematics | Algebra - General |
| Dewey: 516.352 |
| LCCN: 00048547 |
| Physical Information: 0.84" H x 6.43" W x 9.56" (1.26 lbs) 272 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |