Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds

@inproceedings{Hardin2004MinimalRE,
  title={Minimal Riesz energy point configurations for rectifiable d-dimensional manifolds},
  author={Douglas P. Hardin and Edward B. Saff},
  year={2004}
}
We investigate the energy of arrangements of N points on a rectifiable d-dimensional manifold A ⊂ Rd that interact through the power law (Riesz) potential V = 1/rs, where s > 0 and r is Euclidean distance in Rd . With Es(A,N) denoting the minimal energy for such N -point configurations, we determine the asymptotic behavior (as N →∞) of Es(A,N) for each fixed s ≥ d. Moreover, if A has positive d-dimensional Hausdorff measure, we show that N -point configurations on A that minimize the s-energy… CONTINUE READING
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