Polarization problem on a higher-dimensional sphere for a simplex

DOI10.1007/s00454-021-00308-1zbMath1485.52006arXiv2003.02165OpenAlexW3182557455MaRDI QIDQ2117353

Sergiy V. Borodachov

Publication date: 21 March 2022

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.02165

zbMATH Keywords

potentialspheresimplexgeneralized Chebyshev constantmaximal polarizationoptimal covering problem

Mathematics Subject Classification ID

Spherical and hyperbolic convexity (52A55) Packing and covering in (n) dimensions (aspects of discrete geometry) (52C17) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (3)

Absolute minima of potentials of certain regular spherical configurations ⋮ Odd strength spherical designs attaining the Fazekas-Levenshtein bound for covering and universal minima of potentials ⋮ On polarization of spherical codes and designs

Cites Work

• Unnamed Item
• Unnamed Item
• On extremums of sums of powered distances to a finite set of points
• Riesz polarization inequalities in higher dimensions
• On the sum of powered distances to certain sets of points on the circle
• Asymptotically optimal configurations for Chebyshev constants with an integrable kernel
• The sum of the distances to certain pointsets on the unit circle
• The sum of the distances to N points on a sphere
• Covering and separation of Chebyshev points for non-integrable Riesz potentials
• Unconstrained polarization (Chebyshev) problems: basic properties and Riesz kernel asymptotics
• Polarization, sign sequences and isotropic vector systems
• Polarization optimality of equally spaced points on the circle for discrete potentials
• Transfinite diameter, Chebyshev constant and energy on locally compact spaces
• Potential theoretic approach to rendezvous numbers
• Asymptotics of discrete Riesz \(d\)-polarization on subsets of \(d\)-dimensional manifolds
• Multiple packings and coverings of the sphere
• Optimal discrete measures for Riesz potentials
• A minimax problem for sums of translates on the torus
• Chebyshev constants for the unit circle
• Discrete Energy on Rectifiable Sets
• On Various Definitions of Capacity and Related Notions

This page was built for publication: Polarization problem on a higher-dimensional sphere for a simplex