1 citations · 1 across the 6 of their papers we have counts for
7 papers
Alexander-Taylor's inequality for capacities in complex Sobolev spaces
Ngoc Cuong Nguyen, Do Duc Thai
We prove a sharp inequality between the Alexander-Taylor capacity and the functional capacity in a complex Sobolev space on a compact Kähler manifold. The latter space and capacity…
Polar sets for -subharmonic functions on compact Hermitian manifolds
Slawomir Kolodziej, Ngoc Cuong Nguyen
We prove a sharp decay of capacity of sublevel sets of a -subharmonic functions on a -dimensional compact Hermitian manifold which generalizes the case as w…
A remark on the Hölder regularity of solutions to the complex Hessian equation
Slawomir Kolodziej, Ngoc Cuong Nguyen
We prove that the Dirichlet problem for the complex Hessian equation has the Hölder continuous solution provided it has a subsolution with this property. Compared to the previous r…
Complex Hessian measures with respect to a background Hermitian form
Slawomir Kolodziej, Ngoc Cuong Nguyen
We develop potential theory for -subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defin…
Regularity of the Siciak-Zaharjuta extremal function on compact Kähler manifolds
Ngoc Cuong Nguyen
We prove that the regularity of the extremal function of a compact subset of a compact Kähler manifold is a local property, and that the continuity and Hölder continuity are equiva…
The complex Sobolev Space and Hölder continuous solutions to Monge-Ampère equations
Tien-Cuong Dinh, Slawomir Kolodziej, Ngoc Cuong Nguyen
Let be a compact Kähler manifold of dimension and a Kähler form on . We consider the complex Monge-Ampère equation , where is a given positive me…