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

DOI10.1016/j.jco.2023.101742OpenAlexW4321438837MaRDI QIDQ2693694

Ujué Etayo, Pedro R. López-Gómez, Carlos Beltran

Publication date: 24 March 2023

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.08086

zbMATH Keywords

constructive spherical pointsminimal logarithmic energyminimal Green energyconstructive projective points

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities and extremum problems involving convexity in convex geometry (52A40) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Packing and covering in (2) dimensions (aspects of discrete geometry) (52C15) Discrete potential theory (31C20) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (1)

A lower bound for the logarithmic energy on \(\mathbb{S}^2\) and for the Green energy on \(\mathbb{S}^n\)

Uses Software

• SageMath

Cites Work

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• Universal lower bounds for potential energy of spherical codes
• Spherical codes and designs
• On the maximal product of distances between points on a sphere
• Mathematical problems for the next century
• Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere
• On maximal antipodal spherical codes with few distances
• Discrete and continuous Green energy on compact manifolds
• Designs in Grassmannian spaces and lattices
• Minimal discrete energy on the sphere
• Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy
• The Diamond ensemble: a constructive set of spherical points with small logarithmic energy
• Distributing many points on spheres: minimal energy and designs
• Complexity of Bezout's theorem. III: Condition number and packing
• Spherical cap discrepancy of the diamond ensemble
• Some upper bounds in the theory of irregularities of distribution
• Sums of distances between points on a sphere — an application of the theory of irregularities of distribution to discrete Geometry
• Optimal logarithmic energy points on the unit sphere
• Packing Lines, Planes, etc.: Packings in Grassmannian Spaces
• Floating Wigner crystal and periodic jellium configurations
• Discrete Energy on Rectifiable Sets
• A Comparison of Popular Point Configurations on $\mathbb{S}^2$
• The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere

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