A priori $L^{\infty}$-estimates for degenerate complex Monge-Ampère equations

Philippe Eyssidieux (1) , Vincent Guedj (2, 3) , Ahmed Zeriahi (2)

1 IF - Institut Fourier
2 LEP - Laboratoire Émile Picard
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We study families of complex Monge-Ampère equations, focusing on the case where the cohomology classes degenerate to a non big class. We establish uniform a priori $L^{\infty}$-estimates for the normalized solutions, generalizing the recent work of S. Kolodziej and G. Tian. This has interesting consequences in the study of the Kähler-Ricci flow.

Domaines: Géométrie algébrique [math.AG]

Philippe Eyssidieux, Vincent Guedj, Ahmed Zeriahi. A priori $L^{\infty}$-estimates for degenerate complex Monge-Ampère equations. 2007. ⟨hal-00360763⟩