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Disc formulas for the weighted Siciak-Zahariuta extremal function

100%
Magnússon B., Sigurdsson R.
Annales Polonici Mathematici
|
2007
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tom 91
|
nr 2-3
241-247
EN
We prove a disc formula for the weighted Siciak-Zahariuta extremal function $V_{X,q}$ for an upper semicontinuous function q on an open connected subset X in ℂⁿ. This function is also known as the weighted Green function with logarithmic pole at infinity and weighted global extremal function.
2
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Siciak-Zahariuta extremal functions and polynomial hulls

100%
Lárusson F., Sigurdsson R.
Annales Polonici Mathematici
|
2007
|
tom 91
|
nr 2-3
235-239
EN
We use our disc formula for the Siciak-Zahariuta extremal function to characterize the polynomial hull of a connected compact subset of complex affine space in terms of analytic discs.
3
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The Siciak-Zahariuta extremal function as the envelope of disc functionals

100%
Lárusson F., Sigurdsson R.
Annales Polonici Mathematici
|
2005
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tom 86
|
nr 2
177-192
EN
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.
4
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Convexity of sublevel sets of plurisubharmonic extremal functions

81%
Lárusson F., Lassere P., Sigurdsson R.
Annales Polonici Mathematici
|
1998
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tom 68
|
nr 3
267-273
EN
Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_{E,X}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_{E,X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.
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