Yamabe flow

Summary

The Yamabe flow is an evolution equation for a Riemannian metric. The metric changes in the direction of minus its scalar curvature times itself. Richard Hamilton introduced it as a tool for the Yamabe problem. This problem asks for a metric of constant scalar curvature in a given conformal class. The flow keeps the metric in its conformal class. Its fixed points, after normalizing the volume, are the metrics of constant scalar curvature.