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<p>We prove a uniform local non-collapsing volume estimate for a large family of singular metrics in the big cohomology classes, which are Kähler on an open Euclidean subset of the manifold. The key ingredient is a generalization of a mixed energy estimate for functions in the complex Sobolev space to the setting of big cohomology classes.</p>

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Non-collapsing volume estimate for local Kähler metrics in big cohomology classes

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Thai Duong Do,
  • Duc-Bao Nguyen,
  • Duc-Viet Vu

摘要

We prove a uniform local non-collapsing volume estimate for a large family of singular metrics in the big cohomology classes, which are Kähler on an open Euclidean subset of the manifold. The key ingredient is a generalization of a mixed energy estimate for functions in the complex Sobolev space to the setting of big cohomology classes.