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

Nihat Gokhan Gogus; Sonmez Sahutoglu

doi:10.1142/s0129167x12501248

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arXiv · 1107.5500

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

Nihat Gokhan Gogus·Sonmez Sahutoglu

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Abstract

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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Nihat Gokhan Gogus, Sonmez Sahutoglu. 2011-07-27. Continuity of Plurisubharmonic Envelopes in $\mathbb{C}^2$. https://doi.org/10.1142/s0129167x12501248

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