arXiv subjects
Publications and source records attributed to Hoang Van Can.
This paper studies the complex Monge-Ampère equations for $\mathcal F$-plurisubharmonic functions in bounded $\mathcal F$-hyperconvex domains. We give sufficient conditions for this equation to solve for measures with a singular part.
Let $μ$ be a non-negative measure defined on bounded $\mathcal F$-hyperconvex domain $Ω$. We are interested in giving sufficient conditions on $μ$ such that we can find a plurifinely plurisubharmonic function satisfying $NP (dd^c u)^n =μ$ in $QB(Ω)$.
In this note, we study the approximation of singular plurifinely plurisubharmonic function $u$ defined on a plurifinely domain $Ω$. Under some conditions, we prove that $u$ can be approximated by an increasing sequence of plurisubharmonic functions defined on Euclidean neighborhoods of $Ω$.