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Ricci Flow
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For a Riemannian manifold the RICCI FLOW is a partial differential
equation that evolves the metric tensor over 'time'. It is analogous
to the diffusion of heat.
∂g_{μν}(t)/∂t = -2R_{μν}(g_{μν}(t))
The idea is to smooth out irregularities in the metric and make the
geometry of the manifold more symmetric. Informally, it can be
considered as the process of stretching the metric in directions of
negative Ricci curvature, and contracting the metric in directions
of positive Ricci curvature thereby increasing or decreasing the
distance between points on the manifold. The greater the curvature,
the faster the stretching or contracting. Changing the distances
also impacts the angle and area. However, in 2 dimensions the
Ricci flow is conformal meaning that angle does not change with
the flow.