Evgeny A. Poletsky
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.
ArXiv: 1812.09277