Five Point Energy Minimization: A Synopsis

被引：3
|
作者：
Schwartz, Richard Evan [1 ]
机构：
[1] Brown Univ, Dept Math, 151 Thayer St, Providence, RI 02912 USA
来源：
CONSTRUCTIVE APPROXIMATION | 2020年 / 51卷 / 03期
关键词：
Thomson's problem; Energy minimization; Computer proof; CONFIGURATIONS;
D O I：
10.1007/s00365-020-09500-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is a condensation of my arXiv monograph entitled Schwartz "The phase transition in 5 point energy minimization", 2016. arXiv:1610.03303, which contains a complete proof that there is a constant 15.0488 such that the triangular bi-pyramid is the minimizer, amongst all 5 point configurations on the sphere, with respect to the power law potential Rs (r) = sign(s)/r s, if and only if s. (-2, 0). (0,.]. In this paper we explain the main ideas and give proofs for some of the key lemmas.
引用
收藏
页码：537 / 564
页数：28
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