A model Einstein metric on complex hyperbolic branched covers, built the way Fine and Premoselli built theirs in the real hyperbolic case, is shown to equal the model Kähler-Einstein metric of Guenancia and Hamenstädt and to produce negatively curved Einstein metrics in every complex dimension.
Equations du type Monge-Amp` ere sur les v ari´ et´ es K¨ ahleriennes compactes
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An explicit description of the K\"{a}hler-Einstein metrics of Guenancia-Hamenst\"{a}dt
A model Einstein metric on complex hyperbolic branched covers, built the way Fine and Premoselli built theirs in the real hyperbolic case, is shown to equal the model Kähler-Einstein metric of Guenancia and Hamenstädt and to produce negatively curved Einstein metrics in every complex dimension.