Monge-Ampere measures on subvarieties
  In this article we address the question whether the complex Monge-Amp\`{e}re equation is solvable for measures with large singular part. We prove that under some conditions there are no solution when the right-hand side is carried by a smooth subvariety in $\CEP{n}$ of dimension $k<n$. 
Per Ahag, Urban Cegrell and Pham Hoang Hiep
math.CV