Uniform diameter estimates for Kaehler metrics

Duc-Viet Vu

Uniform diameter estimates for Kaehler metrics

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

Uniform diameter estimates for Kaehler metrics

Duc-Viet Vu This is my paper

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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 1 Pith paper

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Complex Monge-Amp\`ere equation in Orlicz space and Diameter Bound
math.DG 2026-01 conditional novelty 6.0

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.