In differential geometry, the Yamabe flow is an intrinsic geometric flow—a process which deforms the metric of a Riemannian manifold.
First introduced by Richard S. Hamilton,[1] Yamabe flow is for noncompact manifolds, and is the negative L2-gradient flow of the (normalized) total scalar curvature, restricted to a given conformal class: it can be interpreted as deforming a Riemannian metric to a conformal metric of constant scalar curvature, when this flow converges.
The fixed points of the Yamabe flow are metrics of constant scalar curvature in the given conformal class.
[2] Later, Simon Brendle proved convergence of the flow for all conformal classes and arbitrary initial metrics.
[3] The limiting constant-scalar-curvature metic is typically no longer a Yamabe minimizer in this context.