在球面上分布多点：最小能量和设计
Distributing many points on spheres: minimal energy and designs
摘要：
本调查讨论了最近的事态发展的背景下，球形设计和最小能量点配置领域。本文给出了A. Bondarenko，D. Radchenko和M.维亚佐夫斯卡引起了人们对这一问题的新兴趣。其次，D. P。哈丁和E。B. Saff证明了在超奇异情形下，使$\mathbb{S}^d$上的离散Riesz能量最小的点集是渐近均匀分布的。这两个结果是非常相关的问题描述的质量点分布在$\mathbb{S}^d$，以及寻找点集，表现出良好的分布行为相对于各种质量措施。
英文摘要：
This survey discusses recent developments in the context of spherical designs and minimal energy point configurations on spheres. The recent solution of the long standing problem of the existence of spherical $t$-designs on $\mathbb{S}^d$ with $\mathcal{O}(t^d)$ number of points by A. Bondarenko, D. Radchenko, and M. Viazovska attracted new interest to this subject. Secondly, D. P. Hardin and E. B. Saff proved that point sets minimising the discrete Riesz energy on $\mathbb{S}^d$ in the hypersingular case are asymptotically uniformly distributed. Both results are of great relevance to the problem of describing the quality of point distributions on $\mathbb{S}^d$, as well as finding point sets, which exhibit good distribution behaviour with respect to various quality measures.
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