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Uniform diameter estimates for Kaehler metrics

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arxiv 2405.14680 v2 pith:MPWFAI5T submitted 2024-05-23 math.DG math.CV

Duc-Viet Vu This is my paper · ORCID
classification math.DGmath.CV
keywords uniformdiameterkaehlermetricsestimateestimatesfamilygeneralizing
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We prove a uniform diameter estimate and a uniform local non-collapsing of volumes for a large family of Kaehler metrics generalizing those obtained recently by Guo-Phong-Song-Sturm. We treat also similar questions in the singular setting.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nash entropy, Calabi energy and geometric regularization of singular K\"ahler metrics

    math.DG 2025-02 conditional novelty 8.0 of 10

    Singular Kähler metrics with Ricci curvature bounded below and rational cohomology class induce non-collapsed RCD spaces homeomorphic to the projective variety, under a resolution condition on the anti-canonical bundle.

  2. Complex Monge-Amp\`ere equation in Orlicz space and Diameter Bound

    math.DG 2026-01 conditional novelty 6.0 of 10

    Under general Orlicz-space integrability of the Monge-Ampère measure, the paper proves L∞ and stability estimates for the potential and derives uniform diameter and volume lower bounds for the associated Kähler metrics.

  3. Uniform estimates: from Yau to Kolodziej

    math.DG 2025-02 accept novelty 6.0 of 10

    A new envelope-based reduction proves uniform a priori estimates from Yau's L^p bound, recovering and extending Kolodziej's Orlicz-type criterion.

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