arXiv subjects
Publications and source records attributed to Slawomir Dinew.
We discuss pluripotential aspects of the Monge-Ampère equations on compact Hermitian manifolds and prove $L^{\infty}$ estimates for any metric, as well as the existence of weak solutions under an extra assumption.
The aim of this note is to study the convergence in capacity for functions in the class $\mathcal E(X,ω)$. We obtain several stability theorems. Some of these are (optimal) generalizations of results of Xing, while others are new.
It is proved that solutions of the complex Monge-Ampère equation on compact Kähler manifolds with right hand side in $L^p, p>1$ are uniformly Hölder continuous under the assumption on non-negative orthogonal bisectional curvature.
We generalize an inequality for mixed Monge-Ampère measures. We also give an example that shows that our assumptions are sharp. The corresponding result in the setting of compact Kähler manifold is also discussed.