This paper demonstrates a uniform local volume estimate for Kähler metrics in big cohomology classes, suggesting significant implications for complex geometry.
We prove a uniform local non-collapsing volume estimate for a large family of K\"ahler metrics in the big cohomology classes. 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.
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Do et al. (2025) studied this question.
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