LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres Academic Article uri icon

abstract

  • Let S{double-struck}d denote the unit sphere in the Euclidean space R{double-struck}d+1(d≥1). We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on S{double-struck}d. We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on S{double-struck}d. © 2010 Elsevier Inc.

author list (cited authors)

  • Narcowich, F. J., Sun, X., Ward, J. D., & Wu, Z.

citation count

  • 7

publication date

  • June 2010