论文标题
相对双曲空间之间的地图和边界之间
Maps between relatively hyperbolic spaces and between their boundaries
论文作者
论文摘要
我们研究了相对双曲基团/空间之间地图与边界之间的准对称嵌入之间的关系。更具体地说，我们在相对柔和的群体/空间之间建立了（不一定要粗糙的）准时嵌入（不一定要尖端的），尊重外围设备的相对双曲线/空间与满足适当条件的边界之间的准对称嵌入。此外，我们建立了与大多数多项式失真的地图相似的对应关系。 我们将其用来表征相对于某些虚拟尼尔氏型亚组的双曲线的组，因为这些组正是那些将嵌入到截断的实际双曲线空间中的组，最多在多种方面的变形中，这是Bonk和Schramm的结果。
We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective) quasi-isometric embeddings between relatively hyperbolic groups/spaces that coarsely respect peripherals, and quasisymmetric embeddings between their boundaries satisfying suitable conditions. Further, we establish a similar correspondence regarding maps with at most polynomial distortion. We use this to characterise groups which are hyperbolic relative to some collection of virtually nilpotent subgroups as exactly those groups which admit an embedding into a truncated real hyperbolic space with at most polynomial distortion, generalising a result of Bonk and Schramm for hyperbolic groups.
