Duc-Viet Vu

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20242026

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math.DG2026

Non-collapsing volume estimate for local KÃ¤hler metrics in big cohomology classes

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

We prove a uniform local non-collapsing volume estimate for a large family of singular metrics in the big cohomology classes, which are KÃ¤hler on an open Euclidean subset of the m…

math.DG2025

KÃ¤hler--Einstein metrics on quasi-projective manifolds

Quang-Tuan Dang, Duc-Viet Vu

Let $X$ be a compact KÃ¤hler manifold and $D$ be a simple normal crossing divisor on $X$ such that $K_{X} + D$ is big and nef. We first prove that the singular KÃ¤hler--Einstein metric…

math.DG2024

Uniform diameter estimates for Kaehler metrics in big cohomology classes

Duc-Bao Nguyen, Duc-Viet Vu

We generalize previous diameter estimates and local non-vanishing of volumes for Kaehler metrics to the case of big cohomology classes. In our proof, among other things, we will pr…