Low-energy points on the sphere and the real projective plane

We present a generalization of a family of points on S2, the Diamond ensemble, containing collections of N points on S2 with very small logarithmic energy for all N∈N. We extend this construction to the real projective plane RP2 and we obtain upper and lower bounds with explicit constants for the Gr...

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Bibliographic Details
Published inJournal of Complexity Vol. 76; p. 101742
Main Authors Beltrán, Carlos, Etayo, Ujué, López-Gómez, Pedro R.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.06.2023
Subjects
Constructive projective points
Constructive spherical points
Minimal Green energy
Minimal logarithmic energy
52A40
31C12
Minimal Green energy
31C20
52C15
Constructive projective points
Minimal logarithmic energy
41A60
52C35
Constructive spherical points
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Summary:We present a generalization of a family of points on S2, the Diamond ensemble, containing collections of N points on S2 with very small logarithmic energy for all N∈N. We extend this construction to the real projective plane RP2 and we obtain upper and lower bounds with explicit constants for the Green and logarithmic energy on this last space.
ISSN:0885-064X
1090-2708
DOI:10.1016/j.jco.2023.101742