Non-collapsing volume estimate for local Kähler metrics in big cohomology classes (2502.16136v1)

Published 22 Feb 2025 in math.DG and math.CV

Abstract: 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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