Mathematische Zeitschrift

, Volume 235, Issue 1, pp 111–122

Certain classes of pluricomplex Green functions on ${\mathbb C}^n$

  • Dan Coman
Original article

DOI: 10.1007/s002090000126

Cite this article as:
Coman, D. Math Z (2000) 235: 111. doi:10.1007/s002090000126


We consider (pluricomplex) Green functions defined on \({\mathbb C}^n\), with logarithmic poles in a finite set and with logarithmic growth at infinity. For certain sets, we describe all the corresponding Green functions. The set of these functions is large and it carries a certain algebraic structure. We also show that for some sets no such Green functions exist. Our results indicate the fact that the set of poles should have certain algebro-geometric properties in order for these Green functions to exist.

Mathematics Subject Classification (1991): 32F05, 32F07, 31C10 

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Dan Coman
    • 1
  1. 1.Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA (e-mail:

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