论文标题
在无穷大的星星的不对称上
On the asymmetry of stars at infinity
论文作者
论文摘要
鉴于有一个接壤的空间，卡尔森定义了无穷大的恒星的发生率。当空间是双曲线，猫（0）或带有希尔伯特度量的有界凸形域时，这些恒星及其发病率与被理解的物体密切相关。卡尔森原始论文提出的一个问题是，一个边界点的关系是否包含在另一个边界点的恒星中是对称的。本文提供了一个示例，证明了三个树diestel-Leader图$ dl_3（q）$的星形边界中的这种关系不是对称的。在此过程中，使用了一些有趣的范围，以diestel-Leader图中的距离。
Given a bordified space, Karlsson defines an incidence geometry of stars at infinity. These stars and their incidence are closely related to well-understood objects when the space is hyperbolic, CAT(0), or a bounded convex domain with the Hilbert metric. A question stemming from Karlsson's original paper was whether or not the relation of one boundary point being included in a star of another boundary point is symmetric. This paper provides an example demonstrating that this relation in the star boundary of the three-tree Diestel-Leader graph $DL_3(q)$ is not symmetric. In doing so, some interesting bounds on distance in Diestel-Leader graphs are utilized.
