Ricci Iteration for Coupled Kähler-Einstein Metrics

In this paper, we introduce the coupled Ricci iteration , a dynamical system related to the Ricci operator and twisted K hler Einstein metrics as an approach to the study of coupled K hler Einstein (CKE) metrics. For negative 1st Chern class, we prove the smooth convergence of the iteration. For positive 1st Chern class, we also provide a notion of coercivity of the Ding functional and show its equivalence to the existence of CKE metrics. As an application, we prove the smooth convergence of the iteration on CKE Fano manifolds assuming that the automorphism group is discrete.