Eyssidieux, Philippe; Guedj, Vincent; Zeriahi, Ahmed A priori \(L^{\infty}\)-estimates for degenerate complex Monge-Ampère equations. (English) Zbl 1162.32020 Int. Math. Res. Not. 2008, Article ID rnn070, 8 p. (2008). Summary: We study families of complex Monge-Ampère equations, focusing on the case where the cohomology classes degenerate to a nonbig class. We establish uniform a priori \(L^{\infty}\)-estimates for the normalized solutions, generalizing the recent work of S. Kolodziej and G. Tian [Math. Ann. 342, No. 4, 773–787 (2008; Zbl 1159.32022)]. This has interesting consequences in the study of the Kähler-Ricci flow. Cited in 25 Documents MSC: 32W20 Complex Monge-Ampère operators 32Q15 Kähler manifolds 35J60 Nonlinear elliptic equations Keywords:cohomology classes; nonbig class; Kähler-Ricci flow Citations:Zbl 1159.32022 PDFBibTeX XMLCite \textit{P. Eyssidieux} et al., Int. Math. Res. Not. 2008, Article ID rnn070, 8 p. (2008; Zbl 1162.32020) Full Text: DOI arXiv