论文标题
凸体的质心及其投影的质心可以相距多远？
How far apart can the projection of the centroid of a convex body and the centroid of its projection be?
论文作者
论文摘要
我们表明，有一个恒定的$ d \约0.2016 $，以便每$ n $，每个凸件$ k \ subset \ subset \ mathbb r^n $，以及每个超平面$ h \ subset \ subset \ mathbb r^n $，$ k $ the $ k $ $ k $ $ k $ y $ k $ k $ h $ k $ h $的距离连接两个点的段的方向。常数$ d $在渐近上是敏锐的。
We show that there is a constant $D \approx 0.2016$ such that for every $n$, every convex body $K\subset \mathbb R^n$, and every hyperplane $H\subset \mathbb R^n$, the distance between the projection of the centroid of $K$ onto $H$ and the centroid of the projection of $K$ onto $H$ is at most $D$ times the width of $K$ in the direction of the segment connecting the two points. The constant $D$ is asymptotically sharp.
