In differential geometry, the Yamabe flow is an intrinsic geometric flow—a process which deforms the metric of a Riemannian manifold. It 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.

It was introduced by Richard Hamilton shortly after the Ricci flow, as an approach to solve the Yamabe problem on manifolds of positive conformal Yamabe invariant.