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.
Famous quotes containing the word flow:
“For as the interposition of a rivulet, however small, will occasion the line of the phalanx to fluctuate, so any trifling disagreement will be the cause of seditions; but they will not so soon flow from anything else as from the disagreement between virtue and vice, and next to that between poverty and riches.”
—Aristotle (384–322 B.C.)