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

Beltrán Álvarez, Carlos; Etayo Rodríguez, Ujué; López Gómez, Pedro Ramón

doi:10.1016/j.jco.2023.101742

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Identificadores

URI: https://hdl.handle.net/10902/31928

DOI: 10.1016/j.jco.2023.101742

ISSN: 0885-064X

ISSN: 1090-2708

Fecha

2023-06

Derechos

Publicado en

Journal of Complexity, 2023, 76, 101742

Editorial

Elsevier

Enlace a la publicación

https://doi.org/10.1016/j.jco.2023.101742

Palabras clave

Constructive projective points

Constructive spherical points

Minimal Green energy

Minimal logarithmic energy

Resumen/Abstract

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.

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© 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Excepto si se señala otra cosa, la licencia del ítem se describe como © 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).