Uniform diameter estimates for Kaehler metrics
Duc-Viet Vu
TL;DR
This paper establishes uniform diameter bounds and volume non-collapsing results for a broad class of Kähler metrics, extending recent work and addressing singular cases.
Contribution
It provides new uniform estimates for Kähler metrics, including in singular settings, broadening the understanding of their geometric properties.
Findings
Proved uniform diameter bounds for a large family of Kähler metrics.
Established uniform local non-collapsing volume estimates.
Extended results to singular Kähler metrics.
Abstract
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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Taxonomy
TopicsGeometry and complex manifolds · Advanced Mathematical Physics Problems · Geometric Analysis and Curvature Flows