A Priori L -Estimates for Degenerate Complex Monge-Ampere Equations

P. Eyssidieux, V. Guedj, A. Zeriahi
2010 International mathematics research notices  
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 ∞ -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.
doi:10.1093/imrn/rnn070 fatcat:3ucatv333fc5hmf5gny3a6uho4