Abstract: Motivated by the problem of finding constant scalar curvature Kahler (cscK) metrics, we investigate a Ricci iteration sequence of Rubinstein that discretizes some generalized version of the Kahler Ricci flow. While the long time existence of the flow is still an open question, we show that the iteration sequence does exist for all steps, along which the K-energy decreases. We further show, that the iteration sequence (modulo automorphisms) converges smoothly to a cscK metric if there is one, thus confirming a conjecture of Rubinstein from 2007.
