On smoothing of plurisubharmonic functions on unbounded domains

2021/04/29 by Harz, Tobias
#32T99 #32U99 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.14448

Abstract

We prove that for every n ≥ 2, there exists a pseudoconvex domain Ω⊂ ℂⁿ such that \mathfrakc⁰(Ω) \subsetneq \mathfrakc¹(Ω), where \mathfrakc^k(Ω) denotes the core of Ω with respect to C^k-smooth plurisubharmonic functions on Ω. Moreover, we show that there exists a bounded continuous plurisubharmonic function on Ω that is not the pointwise limit of a sequence of C¹-smooth bounded plurisubharmonic functions on Ω.

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