Local Maxima of the Potential Energy on Spheres

  • D. V. Radchenko Iн-т математики НАН України, Київ

Abstract

Let S d be a unit sphere in ℝ d+1, and let α be a positive real number. For pairwise different points x 1,x 2, . . . ,x N S d , we consider a functional E α (x 1,x 2, . . . ,x N ) = Σ ij ||x i x j ||α . The following theorem is proved: for αd − 2, the functional E α (x 1,x 2, . . . ,x N ) does not have local maxima.
Published
25.10.2013
How to Cite
RadchenkoD. V. “Local Maxima of the Potential Energy on Spheres”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, no. 10, Oct. 2013, pp. 1427–1429, http://umj.imath.kiev.ua/index.php/umj/article/view/2520.
Section
Short communications