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The curve shortening flow and other closely 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. The first book dedicated to this subject, The Curve Shortening Problem presents a rigorous, comprehensive account of the fundamental results relevant to these flows. With its careful exposition and complete guide to the literature, this book provides both an outstanding starting point for graduate students and a superb reference with intriguing research results for those already active in the field.