轴支外场在球上的最小Riesz能量
Minimal Riesz energy on the sphere for axis-supported external fields
摘要：
研究了在点电荷和线电荷诱导的外场作用下，d维单位球S^d上正测度的最小Riesz s-能量问题.模型的相互作用是Riesz势|X-Y| ^（-s），其中d-2 <= s < d。对于给定的轴支外场，确定了S^d上相应的极值测度的支集和密度。特殊情况s = d-2产生有趣的现象，我们详细研究。当s到达（d-2）^+时，给出了弱 * 渐近分析。
英文摘要：
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)^+.
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