arXiv subjects
Publications and source records attributed to Slawomir Kolodziej.
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.
We prove uniform sup-norm estimates for the Monge-Ampere equation with respect to a family of Kahler metrics which degenerate towards a pull-back of a metric from a lower dimensional manifold. This is then used to show the existence of generalized Kahler-Einstein metrics as the limits of the Kahler-Ricci flow for some holomorphic fibrations (in the spirit of Song and Tian "The Kahler-Ricci flow on surfaces of positive Kodaira dimension", arXiv:math/0602150).
We study the regularity of solutions to complex Monge-Ampère equations $(dd^c u)^n=f dV$, on bounded strongly pseudoconvex domains $ Ω\subset \C^n$. We show, under a mild technical assumption, that the unique solution $u$ to such an equation is Hölder continuous if the boundary values $ϕ$ are Hölder continuous and the density $f$ belongs to $L^p(Ω)$ for some $p>1$. This improves previous results by Bedford-Taylor and Kolodziej.