arXiv subjects
Publications and source records attributed to Szymon Plis.
We show a second order a priori estimate for solutions to the complex $k$-Hessian equation on a compact Kähler manifold provided the $(k$-$1)$-st root of the right hand side is $\mathcal C^{1,1}$. This improves an estimate of Hou-Ma-Wu. An example is provided to show that the exponent is sharp.
We provide an analytic proof of a theorem of Krylov dealing with global $C^{1,1}$ estimates to solutons of degenerate complex Monge-Ampère equations. As an application we show optimal regularity for various extremal functions with nonconstant boundary values.
We show that if $α$ is a positive $(2,2)$-form then so is $α^2$. We also prove that this is no longer true for forms of higher degree.
We study the Dirichlet problem for the Monge-Ampère equation on almost complex manifolds. We obtain the existence of the unique smooth solution of this problem in strictly pseudoconvex domains.