Quasi-uniformity of minimal weighted energy points on compact metric spaces
For a closed subset K of a compact metric space A possessing an alpha-regular measure mu is with it mu(K) > 0, we prove that whenever s > a, any sequence of weighted minimal Riesz s-energy configurations omega(N) = {X-i,N((s))}(i=1)(N) (for 'nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as N grows large. Furthermore, if K is an a-rectifiable compact subset of Euclidean space (a an integer) with positive and finite a-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as N -> infinity) a prescribed positive continuous limit distribution with respect to alpha-dimensional Hausdorff measure. (C) 2011 Elsevier Inc. All rights reserved.
quasi-uniformity separation distance mesh-separation ratio best-packing covering radius minimal riesz energy