For a closed subset K of a compact metric space A possessing an @a-regular measure @m with @m(K)>0, we prove that whenever s>@a, any sequence of weighted minimal Riesz s-energy configurations @w"N={x"i","N^(^s^)}"i"="1^N on K (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->~) a prescribed positive continuous limit distribution with respect to @a-dimensional Hausdorff measure.
['D. P. Hardin', 'E. B. Saff', 'Justin Whitehouse']
Quasi-uniformity of minimal weighted energy points on compact metric spaces