论文标题
CAT（0）多边形复合物为2-MEDIAN
CAT(0) Polygonal Complexes are 2-Median
论文作者
论文摘要
中间空间是空间，其中每三个点之间的三个间隔在一个点相交。众所周知，等级-1仿生建筑物是中间空间，但是由于Haettel，较高的排名建筑物甚至并不是粗糙的中位数。我们定义了``2-median space''的概念，该概念粗略地说，每四个点，最小的圆盘填充了它们跨越一个点或地球段的四个地球三角形。我们表明，CAT（0）欧几里得多边形复合物，尤其是Rank-2仿生建筑物是2-Median。在附录中，我们恢复了fary-Milnor型定理的Stadler结果的特殊情况，并在基本工具中显示出最小的圆盘填充地球三角形的圆盘是注入性的。
Median spaces are spaces in which for every three points the three intervals between them intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but by a result of Haettel, higher rank buildings are not even coarse median. We define the notion of ``2-median space'', which roughly says that for every four points the minimal discs filling the four geodesic triangles they span intersect in a point or a geodesic segment. We show that CAT(0) Euclidean polygonal complexes, and in particular rank-2 affine buildings, are 2-median. In the appendix, we recover a special case of a result of Stadler of a Fary-Milnor type theorem and show in elementary tools that a minimal disc filling a geodesic triangle is injective.
