Local Maxima of the Potential Energy on Spheres

Research paper by D. V. Radchenko

Indexed on: 16 May '14Published on: 16 May '14Published in: Ukrainian Mathematical Journal


Let Sd be a unit sphere in ℝd+1, and let α be a positive real number. For pairwise different points x1,x2, . . . ,xN ∈ Sd, we consider a functional Eα(x1,x2, . . . ,xN) = Σi≠j ||xi − xj||−α. The following theorem is proved: for α ≥ d − 2, the functional Eα(x1,x2, . . . ,xN) does not have local maxima.