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(Pluri)Potential Compactifications

  • Evgeny A. PoletskyEmail author
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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 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.

Keywords

Plurisubharmonic functions Pluripotential theory Martin boundary 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA

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