论文标题
均方根收缩的霍斯赛的收敛性
Convergence of sublinearly contracting horospheres
论文作者
论文摘要
在\ cite {qr19}中，Qing，Rafi和Tiozzo引入了CAT（0）空格的均方根收缩边界。该边界的每个点都以均方根收缩的测量光线为唯一的代表：地球射线$ b $，每个分离球都会向一个子集投射，其直径在球与原点的距离方面受到倍率的功能。本文分析了与此类测量射线相关的呼吸功能的Bahaviour，例如，我们表明与此类呼吸功能相关的hOspheres是收敛的。由于此分析，我们表明，对于任何适当的完整cat（0）空间$ x $，视觉边界的每个点$ \ partial x $由sublinearliearly合同的测地射线定义为一个可见性点。
In \cite{QR19}, Qing, Rafi and Tiozzo introduced the sublinearly contracting boundary for CAT(0) spaces. Every point of this boundary is uniquely represented by a sublinearly contracting geodesic ray: a geodesic ray $b$ where every disjoint ball projects to a subset whose diameter is bounded by a sublinear function in terms of the ball's distance to the origin. This paper analyzes the bahaviour of horofunctions associated to such geodesic rays, for example, we show that horospheres associated to such horofunctions are convergent. As a consequence of this analysis, we show that for any proper complete CAT(0) space $X$, every point of the visual boundary $\partial X$ that is defined by a sublinearly contracting geodesic ray is a visibility point.
