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A priori \(L^{\infty}\)-estimates for degenerate complex Monge-Ampère equations. (English) Zbl 1162.32020

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.

MSC:

32W20 Complex Monge-Ampère operators
32Q15 Kähler manifolds
35J60 Nonlinear elliptic equations

Citations:

Zbl 1159.32022
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