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arXiv · 2403.12867

Balls minimize moments of logarithmic and Newtonian equilibrium measures

Carrie Clark·Richard S. Laugesen
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Abstract

The $q$-th moment ($q>0$) of electrostatic equilibrium measure is shown to be minimal for a centered ball among $3$-dimensional sets of given capacity, while among $2$-dimensional sets a centered disk is the minimizer for $0<q \leq 2$. Analogous results are developed for Newtonian capacity in higher dimensions and logarithmic capacity in $2$ dimensions. Open problems are raised for Riesz equilibrium moments.

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Carrie Clark, Richard S. Laugesen. 2024-03-19. Balls minimize moments of logarithmic and Newtonian equilibrium measures. https://arxiv.org/abs/2403.12867

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