Coupled complex Monge-Ampère equations on Fano horosymmetric manifolds

Abstract

We give necessary and sufficient conditions for existence of solutions to a general system of complex Monge-Ampère equations on Fano horosymmetric manifolds. In particular, we get necessary and sufficient conditions for existence of coupled Kähler-Ricci solitons, Mabuchi metrics and twisted Kähler-Einstein metrics in terms of combinatorial data of the manifold.

accepted version

References in corpus (2)

• Fano threefolds with infinite automorphism groups
• Mabuchi metrics and properness of the modified DING functional

Cited by in corpus (10)

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• Uniform K-stability of polarized spherical varieties
• The Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds
• Ricci iteration for coupled Kähler-Einstein metrics
• Geometric quantization of coupled Kähler-Einstein metrics
• Examples of K-unstable Fano manifolds
• Residue formula for an obstruction to Coupled Kähler-Einstein metrics
• Deformation for coupled Kähler-Einstein metrics
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one