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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 Kähler manifolds using directed positive closed currents. We prove that if a…
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.CV2024
Higher complex Sobolev spaces on complex manifolds
Thai Duong Do, Duc-Bao Nguyen
We study higher complex Sobolev spaces and their corresponding functional capacities. In particular, we prove the Moser-Trudinger inequality for these spaces and discuss some relat…