Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Antonio Trusiani - ,
Titre Séance annulée - Continuity of the Monge- Ampère operator and Kähler-Einsten metrics with prescribed singularities
Horaire14:00 à 15:00

On (X, ω) compact Kähler manifold, I will show that the Monge-Ampère operator is an homeomorphism between a set XA of certain ω-plurisubharmonic functions whose singularities are encoded in a total ordered family A ⊂ PSH(X, ω) representing some singularity types and a set YA of measures. The elements of these sets are characterized by having relative finite energy, so they have natural strong topologies which make the energies continuous. Then I will expose how to deal with complex Monge-Ampère equations with prescribed singularities through a continuity method which also involves the singularities types. As application and main motivation, I will also present how in the Fano case the existence of Kähler-Einstein metrics with prescribed singularities is related to the existence of the genuine Kähler-Einstein metrics.