Complex Monge-Ampere equations with prescribed singularities
Also appears in collection : Constant scalar curvature metrics in Kähler and Sasaki geometry / Métriques à courbure scalaire constante en géométrie Kählérienne et Sasakienne
Since the proof of the Calabi conjecture given by Yau, complex Monge-Ampère equations on compact Kähler manifolds have been intensively studied. In this talk we consider complex Monge-Ampère equations with prescribed singularities. More precisely, we fix a potential and we show existence and uniqueness of solutions of complex Monge-Ampère equations which have the same singularity type of the model potential we chose. This result can be interpreted as a generalisation of Yau’s theorem (in this case the model potential is smooth). As a corollary we obtain the existence of singular Kähler-Einstein metrics with prescribed singularities on general type and Calabi-Yau manifolds. This is a joint work with Tamas Darvas and Chinh Lu.
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