Asymptotics for the minimum Riesz energy and best-packing on sets of finite packing premeasure

• Autores: S.V. Borodachov
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 56, Nº 1, 2012, págs. 225-254
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We show that for every compact set A  Rm of nite -dimensional packing premeasure 0 <  m, the lower limit of the normalized discrete minimum Riesz s-energy (s > ) coincides with the outer measure of A constructed from this limit by method I. The asymptotic behavior of the discrete minimum energy on compact subsets of a self-similar set K satisfying the open set condition is also studied for s greater than the Hausdor dimension of K. In addition, similar problems are studied for the best-packing radius.