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vu viet
  • 750
  • 5
  • 15

maximun of two plurisubharmonic

Let $u,v$ be two plurisubharmonic functions in a domain $\Omega\subset \mathbb{C}^n.$ Then $w=\max$ {$u,v$} is plurisubharmonic. The support of $dd^c w$ is unclear in {$z: u(z)=v(z)$}

How to estimate $dd^c w$ by $dd^c u$ and $dd^c v$? Generally, is there any information on $dd^c$ of a combination of $"max", "min", "+,-"$ operators of a family of plursisubharmonic functions?

vu viet
  • 750
  • 5
  • 15