关于凸体的对称化：再谈黄金分割
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio
摘要：
证明了对任意Minkowski中心的平面凸紧集$C$，$C$和$-C$的调和平均能最优地包含在相同集合的算术平均中当且仅当$C$的Minkowski不对称性至多是黄金分割比$(1+\sqrt{5})/2 \approx 1.618$ .此外，最不对称的这样一组是（最多线性变换）一个特殊的五边形，我们称之为黄金屋。
英文摘要：
We show that for any Minkowski centered planar convex compact set $C$ the Harmonic mean of $C$ and $-C$ can be optimally contained in the arithmetic mean of the same sets if and only if the Minkowski asymmetry of $C$ is at most the golden ratio $(1+\sqrt{5})/2 \approx 1.618$. Moreover, the most asymmetric such set that is (up to a linear transformation) a special pentagon, which we call the golden house.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
