1 citations · 1 across the 10 of their papers we have counts for
14 papers
Comparison principles for local plurisubharmonic potentials on complex manifolds and applications
Thai Duong Do, Pham Hoang Hiep
We prove a weighted comparison principle for local plurisubharmonic potentials in Cegrell's class on an arbitrary complex manifold under suitable boundary and gluing conditions. We…
Local-to-global maximality for plurisubharmonic functions with locally analytic singularities
Thai Duong Do, Pham Hoang Hiep
We prove that a locally maximal plurisubharmonic function on a domain in $\bC^n$, , is maximal if it has locally analytic singularities with a two-sided locally bounded rem…
Sets of cardinality seven are not sum-dominant
Thai Duong Do, Van Thien Nguyen
We give a self-contained elementary proof of the known result that every set of cardinality seven satisfies . The argument adapts Hegarty's method, usi…
Minimal m-subharmonic functions with nonmaximal Hessian measures
Thai Duong Do, Van Thien Nguyen
For every , we construct Hölder continuous functions on the closed unit ball that are minimal in the Cegrell class $\F_m$, although their Hessian measures are not maxi…
Comparison principles for Monge-Ampère measures on pluripolar sets
Thai Duong Do, Hoang Hiep Pham
In this paper, we introduce a notion of singularity comparison for plurisubharmonic functions based on the Bedford--Taylor capacity. We establish comparison principles for the comp…
An existence theorem for non-pluripolar complex Monge-Ampère type equations on hyperconvex domains
Thai Duong Do, Ngoc Thanh Cong Pham
In this paper, we study the non-pluripolar complex Monge-Ampère measure on bounded domains in \( \mathbb{C}^n \). We establish a general existence theorem for a non-pluripolar comp…
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 ma…
A Dirichlet type problem for non-pluripolar complex Monge-Ampère equations
Thai Duong Do, Hoang-Son Do, Van Tu Le +1
In this paper, we study a Dirichlet type problem for the non-pluripolar complex Monge - Ampère equation with prescribed singularity on a bounded domain of . We provid…
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…
On the finite energy classes of quaternionic plurisubharmonic functions
Thai Duong Do, Van Thien Nguyen
We investigate the finite -energy classes of quaternionic plurisubharmonic functions of Cegrell type. We also construct an example to show that the optimal constant in the…
On the weighted m-energy classes
Thai Duong Do, Van Thien Nguyen
In this article, we investigate the weighted subharmonic functions. We shall give some properties of this class and consider its relation to the Cegrell classes. We also pr…
Some remarks on the Cegrell's class
Hoang-Son Do, Thai Duong Do
In this paper, we study the near-boundary behavior of functions in the case where is strictly pseudoconvex. We also introduce a sufficient condition for be…
Complex Monge-Ampère equation in strictly pseudoconvex domains
Hoang-Son Do, Thai Duong Do, Hoang Hiep Pham
We study the complex Monge-Ampère equation in a strictly pseudoconvex domain with the boundary condition , where . We provide a non-trivi…
A comparison theorem for subharmonic functions
Thai-Duong Do
In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can c…