AI 中文总结
引入粗\(r -\)中位数空间概念，是Bowditch粗中位数空间的高阶类似物，在拟等距下稳定。利用凸射影几何工具，证明几类高阶对称空间存在粗\(r -\)中位数，给出诸多不具有Bowditch粗中位数的例子。
AI 中文摘要
我们引入了粗\(r -\)中位数空间的概念，它是Bowditch粗中位数空间的高阶类似物。我们的概念在拟等距下是稳定的，并且当\(r = 1\)时恢复为Bowditch粗中位数。我们证明了几个高阶对称空间族允许粗\(r -\)中位数，其中\(r\)是对称空间的秩。特别是，我们的列表包括许多已知不允许Bowditch粗中位数的例子。我们的主要工具来自凸射影几何，并且我们证明了在所有可除以及拟齐次适当凸域上存在粗高阶中位数。
英文摘要
We introduce a notion of coarse $r$-median spaces that is a higher-rank analog of Bowditch's coarse median spaces. Our notion is stable under quasi-isometries and recovers Bowditch's coarse medians when $r$ equals 1. We prove that several families of higher rank-symmetric spaces admit coarse $r$-medians with $r$ being the rank of the symmetric space. In particular, our list includes plenty of examples that are known to not admit Bowditch's coarse medians. Our main tools come from convex projective geometry, and we prove the existence of coarse higher medians on all divisible as well as quasi-homogeneous properly convex domains.
Comments74 pages. Minor revisions. Comments are welcome!
