Ricci iteration for coupled Kähler-Einstein metrics

Abstract

In this paper, we introduce the "coupled Ricci iteration", a dynamical system related to the Ricci operator and twisted Kähler-Einstein metrics as an approach to the study of coupled Kähler-Einstein (CKE) metrics. For negative first Chern class, we prove the smooth convergence of the iteration. For positive first Chern class, we also provide a notion of coercivity of the Ding functional, and show its equivalence to 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.

arXiv comment18 pages, final version

References in corpus (6)

• Tian's properness conjectures and Finsler geometry of the space of Kahler metrics
• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Greatest lower bounds on the Ricci curvature of Fano manifolds
• Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds
• Coupled Kähler-Ricci solitons on toric Fano manifolds
• Convergence of the Kähler-Ricci iteration

Cited by in corpus (2)

• Geometric quantization of coupled Kähler-Einstein metrics
• Anticanonically balanced metrics and the Hilbert-Mumford criterion for the ${\delta }_m$-invariant of Fujita-Odaka