论文标题
单纯形，交叉聚型和立方体的非中央部分
Non-central sections of the simplex, the cross-polytope and the cube
论文作者
论文摘要
如果超平面到质心的距离相当大，即大于质心到边缘中点的距离大，我们确定常规$ n $ simplex的最大超平面部分。 N-Cube和L_1球的相似结果是通过Moody，Stone，Zach和Zvavitch以及Liu和Tkocz获得的。在这三种情况下，最大的超平面垂直于从质心到顶点的向量。对于较小的距离（在定义明确的范围内），我们表明这些超平面部分至少在局部最大。我们还确定了具有最大周围的单纯形，跨组合和立方体的超平面截面，即与凸体边界的最大体积相交。
We determine the maximal hyperplane sections of the regular $n$-simplex, if the distance of the hyperplane to the centroid is fairly large, i.e. larger than the distance of the centroid to the midpoint of edges. Similar results for the n-cube and the l_1-ball were obtained by Moody, Stone, Zach and Zvavitch and by Liu and Tkocz. The maximal hyperplanes in these three cases are perpendicular to the vectors from the centroid to the vertices. For smaller distances -- in a well-defined range -- we show that these hyperplane sections are at least locally maximal. We also determine the hyperplane sections of the simplex, the cross-polytope and the cube which have maximal perimeter, i.e. maximal volume intersection with the boundary of the convex body.
