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Asymptotics for Energy Minimizing Configurations on \(S^d\)

  • Sergiy V. BorodachovEmail author
  • Douglas P. Hardin
  • Edward B. Saff
Chapter
  • 288 Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

This chapter is devoted to large N asymptotic results for energy and point configurations on the multidimensional sphere \(S^d\) . We begin with a discussion of the property of uniform distribution on the sphere of a sequence of N-point configurations and provide necessary and sufficient conditions for such uniformity in terms of the notion of discrepancy.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sergiy V. Borodachov
    • 1
    Email author
  • Douglas P. Hardin
    • 2
  • Edward B. Saff
    • 2
  1. 1.Department of MathematicsTowson UniversityTowsonUSA
  2. 2.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA

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