Eleonora Di Nezza: Complex Monge-Ampere equations with prescribed singularities​

Abstract: 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.

Recording during the thematic meeting"Constant Scalar Curvature Metrics in Kähler and Sasaki Geometry" the January 18, 2018 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

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