(Pluri)Potential Compactifications

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 wM 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.

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Correspondence to Evgeny A. Poletsky.

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Poletsky, E.A. (Pluri)Potential Compactifications. Potential Anal 53, 231–245 (2020). https://doi.org/10.1007/s11118-019-09766-y

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Keywords

  • Plurisubharmonic functions
  • Pluripotential theory
  • Martin boundary