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"Curvature flows" as a book category covers the mathematical theory and applications of geometric evolution equations in which shapes change over time according to curvature-driven laws (examples include mean curvature flow, Ricci flow, curve shortening flow). Books in this category range from graduate textbooks and monographs that develop the analytic and geometric foundations—differential geometry, nonlinear parabolic PDEs, existence/uniqueness, singularity formation and regularity, and techniques such as monotonicity formulas and surgery—to research collections, lecture notes, and applied works treating numerical methods and real-world uses in image processing, materials science and topology. Typical readers are advanced undergraduates, graduate students and researchers in geometry, analysis and applied mathematics; prerequisite background usually includes Riemannian geometry and PDEs. Historically important topics and figures (e.g., Hamilton, Huisken, Perelman) and the interplay between analysis, topology and computation are common themes across the category.

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