The Curve Shortening Problem

Autorentext
Chou, Kai-Seng; Zhu, Xi-Ping

Klappentext
The curve shortening flow along with other closely related geometric evolution equations serve as mathematical models for applications in diverse areas, such as phase transition, flame front propagation, chemical reaction, mathematical biology, and image processing. The first book dedicated to this subject, The Curve Shortening Problem presents a rigorous, comprehensive account of the fundamental results relevant to these flows.

Zusammenfassung
The curve shortening flow and other related geometric evolution equations serve as mathematical models for applications in diverse areas, such as phase transitions, flame front propagation, chemical reaction, mathematical biology, and image processing. This book offers a comprehensive account of the fundamental results relevant to these flows.

Inhalt
Basic Results. Invariant Solutions for the Curve Shortening Flow. The Curvature-Eikonal Flow for Convex Curves. The Convex Generalized Curve Shortening Flow. The Non-Convex Curve Shortening Flow. A Class of Non-Convex Anisotropic Flows. Embedded Closed Geodesic on Surfaces. The Non-Convex Generalized Curve Shortening Flow. Bibliography.

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