Calabi flow

Summary

The Calabi flow is an evolution of Kähler metrics on a compact complex manifold that stays inside one Kähler class. It moves the Kähler potential with speed equal to the difference between the scalar curvature and its average. Eugenio Calabi introduced it in his work on extremal Kähler metrics. Along the flow the Calabi energy, the squared $L^2$ norm of that difference, does not increase. Its fixed points are the Kähler metrics of constant scalar curvature, so it is a tool for finding such metrics.