5 papers
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…
Non-collapsing volume estimate for local Kähler 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 Kähler on an open Euclidean subset of the m…
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…
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…
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…