94 citations · 268 across the 24 of their papers we have counts for
25 papers
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…
Hölder estimates for degenerate complex Monge-Ampère equations
Bin Guo, Slawomir Kolodziej, Jian Song +1
Uniform and Hölder estimates were proved by the Kolodziej for complex Monge-Ampère equations on compact Kähler manifolds with volume measure with . On the oth…
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…
Weak convergence of Monge-Ampère measures on compact Hermitian manifolds
Slawomir Kolodziej, Ngoc Cuong Nguyen
We give a sufficient condition on a sequence of uniformly bounded -plurisubharmonic functions, being a Hermitian metric, for which the sequence of associated Monge-Ampère me…
Weak solutions to Monge-Ampère type equations on compact Hermitian manifold with boundary
Slawomir Kolodziej, Ngoc Cuong Nguyen
We prove the bounded subsolution theorem for the complex Monge-Ampère type equation, with the right hand side being a positive Radon measure, on a compact Hermitian manifold with b…