Non-collapsing volume estimate for local K\"ahler metrics in big cohomology classes
Differential Geometry
2026-02-25 v2 Complex Variables
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.
Keywords
Cite
@article{arxiv.2502.16136,
title = {Non-collapsing volume estimate for local K\"ahler metrics in big cohomology classes},
author = {Thai Duong Do and Duc-Bao Nguyen and Duc-Viet Vu},
journal= {arXiv preprint arXiv:2502.16136},
year = {2026}
}
Comments
29 pages, last version, to appear in Mathematische Zeitschrift