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CONTINUITY OF PLURISUBHARMONIC ENVELOPES IN ℂ²

NİHAT GÖKHAN GÖĞÜŞ

Sabancı University, Orhanli Tuzla, 34956, Istanbul, Turkey

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and

SÖNMEZ ŞAHUTOĞLU

Department of Mathematics and Statistics, University of Toledo, Toledo, OH 43606, USA

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https://doi.org/10.1142/S0129167X12501248Cited by:2 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 32U15

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