A+ CATEGORY SCIENTIFIC UNIT

The Siciak–Zahariuta extremal function as the envelope of disc functionals

Volume 86 / 2005

Finnur Lárusson, Ragnar Sigurdsson Annales Polonici Mathematici 86 (2005), 177-192 MSC: Primary 32U35. DOI: 10.4064/ap86-2-8

Abstract

We establish disc formulas for the Siciak–Zahariuta extremal function of an arbitrary open subset of complex affine space. This function is also known as the pluricomplex Green function with logarithmic growth or a logarithmic pole at infinity. We extend Lempert's formula for this function from the convex case to the connected case.

Authors

  • Finnur LárussonDepartment of Mathematics
    University of Western Ontario
    London, Ontario N6A 5B7, Canada
    e-mail
  • Ragnar SigurdssonScience Institute
    University of Iceland
    Dunhaga 3, IS-107 Reykjavík, Iceland
    e-mail

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