Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds
Hardin, D. P. ; Saff, E. B.
arXiv, 0311024 / Harvested from arXiv
Text on arXiv
For a compact set A in Euclidean space we consider the asymptotic behavior of optimal (and near optimal) N-point configurations that minimize the Riesz s-energy (corresponding to the potential 1/t^s) over all N-point subsets of A, where s>0. For a large class of manifolds A having finite, positive d-dimensional Hausdorff measure, we show that such minimizing configurations have asymptotic limit distribution (as N tends to infinity with s fixed) equal to d-dimensional Hausdorff measure whenever s>d or s=d. In the latter case we obtain an explicit formula for the dominant term in the minimum energy. Our results are new even for the case of the d-dimensional sphere.
Publié le : 2003-11-14
Classification:  Mathematical Physics,  Mathematics - General Mathematics,  Mathematics - Metric Geometry,  11K41, 70F10, 28A78, 78A30, 52A40 
@article{0311024,
     author = {Hardin, D. P. and Saff, E. B.},
     title = {Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional
  Manifolds},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0311024}
}

Hardin, D. P.; Saff, E. B. Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional
  Manifolds. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0311024/