# $C-$Robin Functions and Applications

## TL;DR

This paper explores $C$-Robin functions within pluripotential theory, generalizing previous results to construct polynomial families that recover extremal functions for certain compact sets in complex space.

## Contribution

It introduces and studies $C$-Robin functions in pluripotential theory and generalizes Bloom's results to construct polynomial families for extremal functions.

## Key findings

- Construction of polynomial families for $C$-extremal functions
- Generalization of Bloom's results to new convex bodies
- Applications to nonpluripolar compact sets in complex space

## 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 $K\subset {\bf C}^d$.