Plurisubharmonic extremal functions, Lelong numbers and coherent ideal sheaves

Finnur Lárusson*, Ragnar Sigurdsson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


We introduce a new type of pluricomplex Green function which has a logarithmic pole along a complex subspace A of a complex manifold X. It is the largest negative plurisubharmonic function on X whose Lelong number is at least the Lelong number of logmax{|f1|, . . . , |fm|}, where f1, . . . , fm are local generators for the ideal sheaf of A. The pluricomplex Green function with a single logarithmic pole or a finite number of weighted poles is a very special case of our construction. We give several equivalent definitions of this function and study its properties, including boundary behaviour, continuity, and uniqueness. This is based on and extends our previous work on disc functionals and their envelopes.

Original languageEnglish
Pages (from-to)1513-1534
Number of pages22
JournalIndiana University Mathematics Journal
Issue number4
Publication statusPublished - 1999

Other keywords

  • Coherent ideal sheaf
  • Complex subspace
  • Disc functional
  • Envelope
  • Extremal function
  • Pluricomplex Green function
  • Plurisubharmonic


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