紧致CAT（0）空间
Tits compact CAT(0) spaces
摘要：
本文研究了CAT（0）度量空间，其对应的Tits边界是紧的.这种空间的突出例子当然是欧几里得空间。然而，存在非平凡测地线完备的CAT（0）空间，其紧的Tits边界远不是平坦的。我们证明了如果这样的空间的等距群作用于余紧空间，则该空间是“尽可能平坦的”，即边界极小子空间一定是平坦的。我们的结果依赖于双曲等距的存在，这本身就是一个问题。因此，我们添加了以下存在性命题的证明：余紧CAT（0）空间要么允许双曲等距，要么允许凸嵌入平面。
英文摘要：
We investigate CAT(0) metric spaces whose associated Tits boundary is compact. Prominent examples of such spaces are of course the euclidean ones. However there exist non trivial geodesically complete CAT(0) spaces with compact Tits boundary that are far from being flat. We show that if the isometry group of such a space acts cocompactly, then the space is "as flat as possible", i.e. the boundary minimal subspace must be flat. Our result relies on the existence of hyperbolic isometries, which is a problem itself. We hence add the proof of the following existence proposition: a cocompact CAT(0) space either admits a hyperbolic isometry or a convex embedded flat plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
