Continuity of plurisubharmonic envelopes in C2
Göğüş, Nihat Gökhan and Şahutoğlu, Sönmez (2012) Continuity of plurisubharmonic envelopes in C2. International Journal of Mathematics, 23 (12). ISSN 0129-167X (Print) 1793-6519 (Online)
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Official URL: http://dx.doi.org/10.1142/S0129167X12501248
We show that in C2 if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubharmonic upper envelopes of functions continuous up to the boundary are continuous on the closure of the domain. Using this result we prove that smooth bounded pseudoconvex Reinhardt domains in C2 are c-regular.
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