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This subtopic introduces the core ideas in geometric evolution equations, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Yamabe-type flows. This topic studies geometric evolution equations in which geometric objects evolve by curvature or related intrinsic quantities.
Used to regularize and classify geometric structures via evolution PDE.
Ricci flows. This topic studies geometric evolution equations in which geometric objects evolve by curvature or related intrinsic quantities.
Used to regularize and classify geometric structures via evolution PDE.
Flows related to complex manifolds. This topic studies geometric evolution equations in which geometric objects evolve by curvature or related intrinsic quantities.
Used to regularize and classify geometric structures via evolution PDE.
Geometric flows on manifolds of metrics. This topic studies geometric evolution equations in which geometric objects evolve by curvature or related intrinsic quantities.
Used to regularize and classify geometric structures via evolution PDE.
Mean curvature flows. This topic studies geometric evolution equations in which geometric objects evolve by curvature or related intrinsic quantities.
Used to regularize and classify geometric structures via evolution PDE.