4 papers · 1 filter
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 com…
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…
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 provi…