Publicacions Matemàtiques

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

Sergiy Borodachov

Full-text: Open access

Abstract

We show that for every compact set $A\subset {\mathbb R}^m$ of finite $\alpha$-dimensional packing premeasure $0<\alpha\leq m$, the lower limit of the normalized discrete minimum Riesz $s$-energy ($s>\alpha$) 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 Hausdorff dimension of $K$. In addition, similar problems are studied for the best-packing radius.

Article information

Source
Publ. Mat., Volume 56, Number 1 (2012), 225-254.

Dates
First available in Project Euclid: 15 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.pm/1323972972

Mathematical Reviews number (MathSciNet)
MR2918189

Zentralblatt MATH identifier
1245.28005

Subjects
Primary: 28A70 28A80: Fractals [See also 37Fxx]
Secondary: 31C99: None of the above, but in this section 74G65: Energy minimization

Keywords
Minimum Riesz energy best-packing $\epsilon$-complexity packing measure and premeasure self-similar set method I

Citation

Borodachov, Sergiy. Asymptotics for the minimum Riesz energy and best-packing on sets of finite packing premeasure. Publ. Mat. 56 (2012), no. 1, 225--254. https://projecteuclid.org/euclid.pm/1323972972


Export citation