Embeddings of Gromov Hyperbolic Spaces
Embeddings of Gromov Hyperbolic Spaces
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DOI：
10.1007/978-1-4419-9675-6_10
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发表时间：
2000-06
影响因子：
2.2
通讯作者：
M. Bonk;O. Schramm
中科院分区：
文献类型：
--
作者：
M. Bonk;O. Schramm
证明了在一定尺度上有界增长的Gromov双曲测地度量空间X与双曲空间的凸子集大致拟等距.如果允许按某个正常数重缩放X的度量，则存在一个嵌入，其中距离至多被一个加性常数扭曲。另一个嵌入定理指出，任一δ-双曲度量空间等距嵌入到完备测地δ-双曲空间中。进一步研究了Gromov双曲空间与其边界的关系。其中一个应用是刻画双曲平面直至粗准等距线。
It is shown that a Gromov hyperbolic geodesic metric spaceXwith bounded growth at some scale is roughly quasi-isometric to a convex subset of hyperbolic space. If one is allowed to rescale the metric ofXby some positive constant, then there is an embedding where distances are distorted by at most an additive constant.Another embedding theorem states that any δ-hyperbolic metric space embeds isometrically into a complete geodesic δ-hyperbolic space.The relation of a Gromov hyperbolic space to its boundary is further investigated. One of the applications is a characterization of the hyperbolic plane up to rough quasi-isometries.