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"Curvature-driven flows" as a book category encompasses works that study the evolution of curves, surfaces, and interfaces whose motion is governed principally by curvature. It covers mathematical foundations (differential geometry, geometric PDEs, existence and regularity theory), canonical model flows (curve shortening, mean curvature, Willmore, Ricci and anisotropic/crystalline flows), numerical and computational methods (level-set, phase-field, finite element), and multidisciplinary applications in materials science, fluid dynamics, image processing, biology (membrane and cell shape evolution) and geometric analysis. Titles in this category range from rigorous research monographs and advanced graduate texts to applied and computational handbooks, unified by their focus on how curvature controls shape change over time and the techniques used to analyze, simulate, and apply those dynamics.

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