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arXiv · 2206.08086

Low energy points on the sphere and the real projective plane

Carlos Beltrán·Ujué Etayo·Pedro R. López-Gómez
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Abstract

We present a generalization of a family of points on $\mathbb{S}^2$, the Diamond ensemble, containing collections of $N$ points on $\mathbb{S}^2$ with very small logarithmic energy for all $N\in\mathbb{N}$. We extend this construction to the real projective plane $\mathbb{RP}^2$ and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.

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Carlos Beltrán, Ujué Etayo, Pedro R. López-Gómez. 2022-06-16. Low energy points on the sphere and the real projective plane. https://doi.org/10.1016/j.jco.2023.101742

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