A survey summarizing that existence of coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds equates to generalized K-polystability conditions.
Berndtsson : A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in K¨ ahler geometry
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On coupled K\"ahler-Einstein metrics and weighted solitons on Fano manifolds
A survey summarizing that existence of coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds equates to generalized K-polystability conditions.