Degenerate complex Monge-Ampère equations over compact Kahler manifolds

Jean-Pierre Demailly (1) , Nefton Pali (2)

1 IF - Institut Fourier
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Ampère equations, and investigate their regularity. This type of equations is precisely what is needed in order to construct Kahler-Einstein metrics over irreducible singular Kahler spaces with ample or trivial canonical sheaf.

Mots clés: Orlicz spaces; Complex Monge-ampère equations; Kahler-Einstein metrics; Closed positive currents; plurisubharmonic functions; Capacities; Orlicz spaces.

Domaines: Variables complexes [math.CV]

Jean-Pierre Demailly, Nefton Pali. Degenerate complex Monge-Ampère equations over compact Kahler manifolds. 2007. ⟨hal-00199790⟩