论文标题
相关的凸形体的对称性：再次获得黄金比率
Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio
论文作者
论文摘要
我们表明，对于任何以Minkowski为中心的平面凸面套件$ c $ $ c $和$ -c $的谐波平均值可以最佳地包含在同一集的算术平均值中，并且仅当Minkowski的$ c $的minkowski不对称的$ c $最多是黄金比率$ $ $ $ $（1+ \ sqrt $ \ sqrt $ sqrt {5} 5}）$ $ $。此外，最不对称的集合（直到线性转换）是一种特殊的五角大楼，我们称之为金屋。
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.
