ricci flow

Input interpretation

Ricci flow

Definition

The Ricci flow equation is the evolution equation d/(d t) g_(i j)(t) = - 2R_(i j) for a Riemannian metric g_(i j), where R_(i j) is the Ricci curvature tensor. Hamilton showed that there is a unique solution to this equation for an arbitrary smooth metric on a closed manifold over a sufficiently short time. Hamilton (1982, 1986) also showed that Ricci flow preserves positivity of the Ricci curvature tensor in three dimensions and the curvature operator in all dimensions.
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