Ricci Iteration for Coupled Kähler-Einstein Metrics

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Abstract

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.

Original languageEnglish
Pages (from-to)15850-15872
Number of pages23
JournalInternational Mathematics Research Notices
Volume2021
Issue number20
DOIs
Publication statusPublished - Oct 1 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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