Calabi flow and projective embeddings

Understand

Let X be a smooth subvariety of CP^N.

• We study a flow, called balancing flow, on the space of projectively equivalent embeddings of X, which attempts to deform the given embedding into a balanced one.
• If L->X is an ample line bundle, considering embeddings via H^0(L^k) gives a sequence of balancing flows.
• We prove that, provided these flows are started at appropriate points, they converge to Calabi flow for as long as it exists.