$C-$Robin Functions and Applications

Norm Levenberg; Sione Ma`u

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arXiv · 1907.10776

$C-$Robin Functions and Applications

Norm Levenberg·Sione Ma`u

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Abstract

We continue the study in the setting of pluripotential theory arising from polynomials associated to a convex body $C$ in $({\bf R}^+)^d$. Here we discuss $C-$Robin functions and their applications. In the particular case where $C$ is a simplex in $({\bf R}^+)^2$ with vertices $(0,0),(b,0),(a,0)$, $a,b>0$, we generalize results of T. Bloom to construct families of polynomials which recover the $C-$extremal function $V_{C,K}$ of a nonpluripolar compact set $K\subset {\bf C}^d$.

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Norm Levenberg, Sione Ma`u. 2019-07-25. $C-$Robin Functions and Applications. https://arxiv.org/abs/1907.10776

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