$L^\infty$-estimates of Kähler-Einstein potentials on stable varieties

Abstract

We study the asymptotic behavior of Kähler-Einstein potentials on stable varieties near the singularities. Using iterated logarithmic functions associated with a defining function of the non-klt locus, we obtain refined lower bounds for the Kähler-Einstein potential, improving previous estimates of Di Nezza-Guedj-Guenancia and Datar-Fu-Song. Under additional assumptions on the log resolution, we also establish upper bounds. The proofs are based on the construction of explicit subsolutions and supersolutions for degenerate complex Monge-Ampère equations together with refined integrability estimates in pluripotential theory.