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"Geometric flows" as a book category covers the theory, methods, and applications of evolution equations that deform geometric objects—metrics, curves, surfaces, and maps—over time according to curvature- or energy-driven laws. Titles in this area treat foundational examples such as Ricci flow, mean curvature flow, curve-shortening flow and harmonic map flow, and examine analytic topics like short- and long-time existence, singularity formation and resolution, monotonicity formulas, and blow-up analysis, as well as numerical schemes and discrete analogues. Books range from introductory graduate texts and problem-driven introductions to advanced research monographs and applied volumes connecting flows to topology (e.g., proofs of geometric conjectures), image processing, materials science and general relativity. Typical readers are graduate students and researchers in differential geometry, PDEs and applied mathematics, and most books assume familiarity with differential geometry, functional analysis and partial differential equations.

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