A counterexample to the strong subadditivity of extremal plurisubharmonic functions (Q1098972)
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scientific article; zbMATH DE number 4038213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to the strong subadditivity of extremal plurisubharmonic functions |
scientific article; zbMATH DE number 4038213 |
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A counterexample to the strong subadditivity of extremal plurisubharmonic functions (English)
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1988
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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.
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extremal plurisubharmonic function
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capacity
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strong subadditivity
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