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$L^\infty$-estimates of Kähler-Einstein potentials on sta...
[Submitted on 23 Jun 2026] · 2026-06-24 · via math updates on arXiv.org

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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.

Submission history

From: Rui Tang [view email]
[v1] Tue, 23 Jun 2026 12:17:46 UTC (47 KB)