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Coupled Kähler–Ricci solitons on toric Fano manifolds
We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled K\"ahler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for existence …