论文标题
均匀化，$ \ partial $ -bilipschitz地图，球形和反转
Uniformization, $\partial$-biLipschitz maps, sphericalization, and inversion
论文作者
论文摘要
我们定义$ \ partial $ -bilipschitz同构均匀度量空间，并表明这些地图始终是Quasimöbius。我们还表明，同构为$ \ partial $ -bilipschitz等于这些空间上的quasihyperbolic指标中的地图bilipschitz。这些主张的证据要求我们统一准纤维标准。我们进一步表明，格罗莫夫双曲线空间的所有可接受的均匀化都是Quasimöbius彼此彼此的，包括基于Gromov边界点的均匀化。然后，使用主要结果，我们表明球形化和反转操作与自然意义上双曲线空间的均匀化兼容。
We define $\partial$-biLipschitz homeomorphisms between uniform metric spaces and show that these maps are always quasimöbius. We also show that a homeomorphism being $\partial$-biLipschitz is equivalent to the map biLipschitz in the quasihyperbolic metrics on these spaces. The proofs of these claims require us to uniformize the quasihyperbolic metric. We further show that all admissible uniformizations of a Gromov hyperbolic space are quasimöbius to one another by the identity map, including those uniformizations that are based at a point of the Gromov boundary. Using the main results we then show that the sphericalization and inversion operations are compatible with uniformization of hyperbolic spaces in a natural sense.
