9 papers
Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes
Quang-Tuan Dang, Lei Zhang, Bin Zhou
In this paper, we establish a stability estimate and a uniform estimate for the modulus of continuity of solutions to the degenerate complex Monge-Ampère equation in big cohomology…
Uniform estimates for complex Monge-Ampère equations: big cohomology classes
Quang-Tuan Dang, Lei Zhang, Bin Zhou
We prove uniform a priori estimates for solutions to degenerate complex Monge--Ampère equations in big cohomology classes, using both auxiliary-function technique developed by Guo,…
Regularity of solutions to Monge--Ampère equations on compact Hermitian manifolds
Quang-Tuan Dang
We study the stability and Hölder continuity of solutions to degenerate complex Monge--Ampère equations associated with a (non-closed) big form on compact Hermitian manifolds. We a…
Modulus of continuity of Monge--Ampère potentials in big cohomology classes
Quang-Tuan Dang, Hoang-Son Do, Hoang Hiep Pham
In this paper, we prove a uniform estimate for the modulus of continuity of solutions to degenerate complex Monge--Ampère equation in big cohomology classes. This improves the prev…
Singularities vs non-pluripolar Monge--Ampère masses
Quang-Tuan Dang, Hoang-Son Do, Hoang Hiep Pham
The aim of this paper is to compare singularities of closed positive currents whose non-pluripolar complex Monge--Ampère masses equal. We also provide a short alternative proof for…
Hermitian null loci
Quang-Tuan Dang
We establish a transcendental generalization of Nakamaye's theorem to compact complex manifolds when the form is not assumed to be closed. We apply the recent analytic technique de…