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arXiv · 2502.16136

Non-collapsing volume estimate for local K\"ahler metrics in big cohomology classes

Thai Duong Do·Duc-Bao Nguyen·Duc-Viet Vu
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Abstract

We prove a uniform local non-collapsing volume estimate for a large family of singular metrics in the big cohomology classes, which are K\"ahler 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.

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Thai Duong Do, Duc-Bao Nguyen, Duc-Viet Vu. 2025-02-22. Non-collapsing volume estimate for local K\"ahler metrics in big cohomology classes. https://arxiv.org/abs/2502.16136

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