论文标题
CAT（0）空间的双曲线模型
Hyperbolic models for CAT(0) spaces
论文作者
论文摘要
我们介绍了两个用于研究CAT（0）空间的新工具：\ Emph {Curtains}，Cubical Explanes的版本；和\ emph {窗帘模型}，曲线图的对应物。这些工具为猫（0）空间提供了新的启示，使我们能够证明rigigities风味的二分法，建立了临界模型等轴测的伊万诺夫风格的刚性定理，可以找到其格罗莫夫在其上的romov边界的等级范围内的视觉范围，并在刻薄的interies interies interies contriper上，并在刻薄的方面表征了他们的刻录，并构成了他们的刻录。最后，我们表明，在所有在CAT（0）空间上正确作用的组上，窗帘模型对于WPD动作都是通用的。
We introduce two new tools for studying CAT(0) spaces: \emph{curtains}, versions of cubical hyperplanes; and the \emph{curtain model}, a counterpart of the curve graph. These tools shed new light on CAT(0) spaces, allowing us to prove a dichotomy of a rank-rigidity flavour, establish Ivanov-style rigidity theorems for isometries of the curtain model, find isometry-invariant copies of its Gromov boundary in the visual boundary of the underlying CAT(0) space, and characterise rank-one isometries both in terms of their action on the curtain model and in terms of curtains. Finally, we show that the curtain model is universal for WPD actions over all groups acting properly on the CAT(0) space.
