A REVERSE THOMSON PROBLEM ON THE UNIT CIRCLE

作者：Leng, Tuo^*; Wu, Yuchi

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 151(1): 327-337.

DOI：10.1090/proc/16110

• Extremal energy
• Thomson's problem
• Inverse problem

Let x(1), x(2), ..., x(n) be n points on the sphere S-2. Determining thew value inf Sigma(1 <= k<j <= n) vertical bar x(k) - x(j)vertical bar(-1), is a long-standing open problem in discrete geometry, which is known as Thomson's problem. In this paper, we propose a reverse problem on the sphere Sd-1 in d-dimensional Euclidean space, which is equivalent to establish the reverse Thomson inequality. In the planar case, we establish two variants of the reverse Thomson inequality. @@@ In addition, we give a proof to the minimal logarithmic energy of x(1), x(2), ..., x(n) and two dimensional Thomson's problem on the unit circle for all integer n >= 2.

• 单位
  上海大学