A counterexample to the strong subadditivity of extremal plurisubharmonic functions |
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| Authors: | Johan Thorbiörnson |
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| Institution: | 1. Department of Mathematics, University of Ume?, S-90187, Ume?, Sweden
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| Abstract: | A simple example is given which shows that one way have $$h_E (z^0 ) + h_F (z^0 ) > h_{E \cup F} (z^0 ) + h_{E \cap F} (z^0 )$$ for some pointz 0∈ω, where $$h_E (z) = \sup \{ u(z):u \in PSH (\Omega ),u \leqslant 0 on E,u \leqslant 1 in \Omega \} ,z \in \Omega ,$$ is the extremal function often studied in complex analysis. |
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