(Pluri)Potential Compactifications

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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 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

Keywords

  • Martin boundary
  • Pluripotential theory
  • Plurisubharmonic functions

ASJC Scopus subject areas

  • Analysis

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