Continuity of Plurisubharmonic Envelopes in $\mathbb{C}^2$

Details Continuity of Plurisubharmonic Envelopes in $\mathbb{C}^2$ Continuity of Plurisubharmonic Envelopes in $\mathbb{C}^2$

2011-07-27

arxiv.org/abs/1107.5500v1

Mathematics

Complex Variables

13 pages

Scientific paper

We show that in $\mathbb{C}^2$ 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 $\mathbb{C}^{2}$ are $c$-regular.

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