We derive the complete asymptotic expansion in terms of powers of N for the Riesz s-energy of N equally spaced points on the unit circle as N â†’âˆž. For s â‰¥ âˆ’2, such points form optimal energy N -pointâ€¦ (More)

We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz s-energy of N points on the unit sphere in Rd+1, dâ€¦ (More)

We study equal weight numerical integration, or Quasi Monte Carlo (QMC) rules, for functions in a Sobolev space Hs(Sd) with smoothness parameter s > d/2 defined over the unit sphere Sd in Rd+1.â€¦ (More)

We study minimum energy point charges on the unit sphere Sd in Rd+1, d â‰¥ 3, that interact according to the logarithmic potential log(1/r), where r is the Euclidean distance between points. Suchâ€¦ (More)

This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres. The recent solution of the long standing problem of the existence ofâ€¦ (More)

Let A be a compact set in the right-half plane and Î“(A) the set in R 3 obtained by rotating A about the vertical axis. We investigate the support of the limit distribution of minimal energy pointâ€¦ (More)

Let A âŠ† R2 be a compact set in the right-half plane and Î“(A) the set in R3 obtained by rotating A about the vertical axis. We review recent results concerning the support of the equilibrium measureâ€¦ (More)

We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S in the presence of an external field induced by a point charge, and more generally by a lineâ€¦ (More)