(Pluri)Potential Compactifications

Evgeny Alexander Poletsky

Research output: Contribution to journal › Article

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 L1(M, V). Moreover, the set of such functions with the norm not exceeding 1 is compact. Identifying a point w ∈ 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.

Original languageEnglish (US)
JournalPotential Analysis
DOIs
StatePublished - Jan 1 2019

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Pluricomplex Green Function
Compactification
Plurisubharmonic Function
Imbedding
Potential Theory
Complex Manifolds
Compact Set
Pole
Closure
Norm
Invariant

Keywords

  • Martin boundary
  • Pluripotential theory
  • Plurisubharmonic functions

ASJC Scopus subject areas

  • Analysis

Cite this

(Pluri)Potential Compactifications. / Poletsky, Evgeny Alexander.

In: Potential Analysis, 01.01.2019.

Research output: Contribution to journal › Article

Poletsky, EA 2019, '(Pluri)Potential Compactifications', Potential Analysis. https://doi.org/10.1007/s11118-019-09766-y
Poletsky EA. (Pluri)Potential Compactifications. Potential Analysis. 2019 Jan 1. https://doi.org/10.1007/s11118-019-09766-y
Poletsky, Evgeny Alexander. / (Pluri)Potential Compactifications. In: Potential Analysis. 2019.
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