A counterexample to the strong subadditivity of extremal plurisubharmonic functions |
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| Authors: | Johan Thorbiörnson |
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| Affiliation: | 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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