论文标题
摩尔斯边界上的地图
Maps on the Morse boundary
论文作者
论文摘要
对于适当的测量公制空间$ x $，莫尔斯边界$ \ partial_*x $着重于空间$ x $的双曲线样方向。这是一个准染色的不变。也就是说，两个双曲空空间之间的准等级法会引起其边界的同态形态。在本文中，我们调查了Morse边界上的其他结构$ \ partial_*x $，这些结构确定了$ x $的准代表。我们证明，对于$ x $和$ y $适当的，共同体的空间，当莫尔斯边界之间的同构$ f $是由准iSometry引起的，并且仅当$ f $ and $ f $ and $ f^{ - 1} $是bihölder或quasi-ymmettricric，或quasi-Mystricric，或Quassi-Mettryly quasi-quasi-conformal。
For a proper geodesic metric space $X$, the Morse boundary $\partial_*X$ focuses on the hyperbolic-like directions in the space $X$. It is a quasi-isometry invariant. That is, a quasi-isometry between two hyperbolic spaces induces a homeomorphism on their boundaries. In this paper, we investigate additional structures on the Morse boundary $\partial_*X$ which determine $X$ up to a quasi-isometry. We prove that, for $X$ and $Y$ proper, cocompact spaces, a homeomorphism $f$ between their Morse boundaries is induced by a quasi-isometry if and only if $f$ and $f^{-1}$ are bihölder, or quasi-symmetric, or strongly quasi-conformal.
