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

Details The Siciak-Zahariuta extremal function as the envelope of disc functionals The Siciak-Zahariuta extremal function as the envelope of disc functionals

2005-04-22

arxiv.org/abs/math/0504471v3

Mathematics

Complex Variables

Version 3 contains a proof of Lempert's formula for the S-Z function in the convex case, in slightly modified form, for an arb

Scientific paper

We establish disc formulas for the Siciak-Zahariuta extremal function of an
arbitrary open subset of complex affine space, generalizing Lempert's formula
for the convex case. 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.

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