Minimal Energy Asymptotics in the “Harmonic Series” Case

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


This chapter deals with the asymptotic behavior of the value of the minimal Riesz d-energy on compact subsets of d-dimensional \(C^1\) manifolds in \(\mathbb R^p\), \(d\le p\). The weak\(^*\)-limit distribution of sequences of energy minimizing configurations and lower estimates of their minimal pairwise separation can be also found here. Finally, a class of sequences of asymptotically d-energy minimizing configurations is constructed for sets of positive d-dimensional Lebesgue measure.

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© 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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