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C-Robin functions and applications

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Abstract

We continue the study in [1] in the setting of pluripotential theory arising from polynomials associated to a convex body C in (ℝ+)d. Here we discuss C-Robin functions and their applications. In the particular case where C is a triangle in (ℝ+)2 with vertices (0, 0), (b, 0), (0, a), a, b > 0, we generalize results of T. Bloom to construct families of polynomials which recover the C-extremal function VC,K of a nonpluripolar compact set K ⊂ ℂ2.

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Acknowledgement

We would like to thank Franck Wielonsky for correcting the formula three lines above (6.3).

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Correspondence to N. Levenberg.

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Supported by Simons Foundation grant No. 354549.

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Levenberg, N., Ma’u, S. C-Robin functions and applications. Anal Math 46, 781–819 (2020). https://doi.org/10.1007/s10476-020-0046-6

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  • DOI: https://doi.org/10.1007/s10476-020-0046-6

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