A counterexample to the strong subadditivity of extremal plurisubharmonic functions
A simple example is given which shows that one may have \[ h_ E(a)+ h_ F(a)> h_{E\cup F}(a)+ h_{E\cap F}(a) \] for some point \(a\in \Omega\), where \[ h_ E(z)=\sup \{u(z): u\in PSH(\Omega),\quad u\leq 0\quad on\quad E,\quad u\leq 1\quad in\quad \Omega \},\quad z\in \Omega, \] is the extremal function often studied.
scientific article; zbMATH DE number 4038213