Duc-Viet Vu

collaborators

6 papers

math.CV2026

Quantitative hyperbolicity for complex manifolds via numerical invariants

Tien-Cuong Dinh, Duc-Bao Nguyen, Duc-Viet Vu

We introduce numerical invariants called hyperbolic indices, which measure the hyperbolicity of compact KÃ¤hler manifolds using directed positive closed currents. We prove that if…

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.CV2025

Singularity of non-pluripolar cohomology classes

Duc-Bao Nguyen, Shuang Su, Duc-Viet Vu

We establish a relation between Lelong numbers and the full mass property of relative non-pluripolar products. We use this relation to prove that if the restricted volume of a big…

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.CV2025

A survey on asymptotic equilibrium distribution of zeros of random holomorphic sections

George Marinescu, Duc-Viet Vu

This is a survey of results concerning the asymptotic equilibrium distribution of zeros of random holomorphic polynomials and holomorphic sections of high powers of a positive line…

math.CV2025

Log continuity of solutions of complex Monge-AmpÃ¨re equations

Hoang-Son Do, Duc-Viet Vu

Let $X$ be a compact KÃ¤hler manifold whose anticanonical cohomology class is semipositive. Let $L$ be a big and semi-ample line bundle on $X$ and $I^\pm$ be the Chern class of $L$ . W…