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Mathematics > Complex Variables

arXiv:1812.09277 (math)
[Submitted on 21 Dec 2018 (v1), last revised 31 Jan 2019 (this version, v2)]

Title:(Pluri)potential compactifications

Authors:Evgeny A. Poletsky
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Abstract:Using pluricomplex Green functions we introduce a compactification of a complex manifold $M$ invariant with respect to biholomorphisms similar to the Martin compactification in the potential theory. For this we show the existence of a norming volume form $V$ on $M$ such that all negative plurisubharmonic functions on $M$ are in $L^1(M,V)$. Moreover, the set of such functions with the norm not exceeding 1 is compact. Identifying a point $w\in M$ with the normalized pluricomplex Green function with pole at $w$ we get an imbedding of $M$ into a compact set and the closure of $M$ in this set is the pluripotential compactification.
Comments: The text improved following referee's suggestion. To appear in "Potential Analysis"
Subjects: Complex Variables (math.CV)
Cite as: arXiv:1812.09277 [math.CV]
  (or arXiv:1812.09277v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1812.09277

Submission history

From: Evgeny Poletsky [view email]
[v1] Fri, 21 Dec 2018 17:36:45 UTC (14 KB)
[v2] Thu, 31 Jan 2019 21:14:49 UTC (14 KB)
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