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arXiv · 2606.24481

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

Rui Tang
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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.

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Rui Tang. 2026-06-23. $L^\infty$-estimates of Kähler-Einstein potentials on stable varieties. https://arxiv.org/abs/2606.24481

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