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This is a Quantitative Study study.

October 11, 2025Open Access

Green's function and volume noncollapsing estimates for the Kähler-Ricci flow

Key Points

Local volume noncollapsing property exists for the long-time kähler-ricci flow on minimal manifolds, enhancing existing results.
New green's function estimates were developed under specific volume density conditions, leading to significant theoretical advancements.
Similar volume noncollapsing results were established for twisted kähler-ricci flow on non-minimal kähler manifolds, broadening the applicability.
The paper's findings support further exploration of geometric properties and evolution in complex manifolds.

Abstract

We prove a local volume noncollapsing property for the long-time Kähler-Ricci flow on a minimal Kähler manifold, improving previous results of Guo-Phong-Song-Sturm, Guedj-Tô and Vu. Similar result is also proved for a twisted Kähler-Ricci flow on non-minimal Kähler manifolds. In the course of proof, we develop new Green's function estimates for a general Kähler family under the L^p>1 and L¹ (L) ^q>n volume density conditions.

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Cite This Study

Zhang et al. (Tue,) studied this question.

synapsesocial.com/papers/68e9b1b5ba7d64b6fc131e10 https://doi.org/https://doi.org/10.48550/arxiv.2508.13646