标题： 轴对称外场下球面上的最小 Riesz 能量 显示英文标题

标题： Minimal Riesz energy on the sphere for axis-supported external fields

摘要： 我们研究在由点电荷以及更一般地由线电荷引起的外部场存在下，d维单位球面S^d上正测度的最小Riesz s-能量问题。 模型相互作用为Riesz势|x-y|^(-s)，其中d-2 ≤ s < d。对于给定的轴支撑的外部场，确定了S^d上相应极值测度的支撑和密度。 特殊情况s = d-2产生有趣的现象，我们对其进行详细研究。 提供了当s趋近于(d-2)^+时的弱*渐近分析。 显示英文摘要

摘要： We investigate the minimal Riesz s-energy problem for positive measures on the d-dimensional unit sphere S^d in the presence of an external field induced by a point charge, and more generally by a line charge. The model interaction is that of Riesz potentials |x-y|^(-s) with d-2 <= s < d. For a given axis-supported external field, the support and the density of the corresponding extremal measure on S^d is determined. The special case s = d-2 yields interesting phenomena, which we investigate in detail. A weak* asymptotic analysis is provided as s goes to (d-2)^+.