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ArticleOriginal scientific text

Title

A constant in pluripotential theory

Authors ¹

Affiliations

Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We compute the constant sup {

(\frac{1}{deg P}) (max_{S} \log | P | - \int_{S} \log | P | d σ)

: P a polynomial in

ℂ^{n}

}, where S denotes the euclidean unit sphere in

ℂ^{n}

and σ its unitary surface measure.

H. Alexander, Projective capacity, in: Ann. of Math. Stud. 100, Princeton Univ. Press, 1981, 3-27.
J.-P. Demailly, Potential theory in several complex variables, preprint, 1989.
W. Rudin, Function Theory in the Unit Ball of $ℂ^{n}$ , Springer, 1980.
J. Siciak, Extremal plurisubharmonic functions and capacities in $ℂ^{n}$ , Sophia Kokyuroku in Math. 14 (1982).