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 language | English (US) |
|---|---|
| Pages (from-to) | 231-245 |
| Number of pages | 15 |
| Journal | Potential Analysis |
| Volume | 53 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jun 1 2020 |
Keywords
- Martin boundary
- Pluripotential theory
- Plurisubharmonic functions
ASJC Scopus subject areas
- Analysis
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Cite this
Poletsky, E. A. (2020). (Pluri)Potential Compactifications. Potential Analysis, 53(1), 231-245. https://doi.org/10.1007/s11118-019-09766-y