五点能量最小化中的相变
最优化与控制
2016-11-22 v3
摘要
令 R_s(r)=sign(s)/r^s 为 Riesz s-能量势（即通常的幂律势）。本专著证明存在一个可计算数 S=15.048...，使得三角双锥是球面上所有五点构型中关于 R_s 的唯一极小化子，当且仅当 s 位于 (-2,0) 或 (0,S) 内。这确立了五点能量最小化中长期猜想的相变常数的存在性。
引用
@article{arxiv.1610.03303,
title = {The Phase Transition in 5 Point Energy Minimization},
author = {Richard Evan Schwartz},
journal= {arXiv preprint arXiv:1610.03303},
year = {2016}
}
备注
This is a rigorous computer-assisted proof. Software is available to download. The proof in this version is identical to the proof in the first two versions. In this version I updated the preface and the introduction to reflect improvements I made to the computer code. Also, I fixed typos in equations 15.7-15.9. The final result from this section (Inequality 1) is unchanged