Journal
GEOMETRIAE DEDICATA
Volume 87, Issue 1-3, Pages 285-307Publisher
SPRINGER
DOI: 10.1023/A:1012093209450
Keywords
Bilipschitz embeddings; metric spaces; doubling property; Gromov hyperbolicity
Categories
Ask authors/readers for more resources
The paper describes some basic geometric tools to construct bilipschitz embeddings of metric spaces into (finite-dimensional) Euclidean or hyperbolic spaces. One of the main results implies the following: If X is a geodesic metric space with convex distance function and the property that geodesic segments can be extended to rays, then X admits a bilipschitz embedding into some Euclidean space X has the doubling property, and X admits a bilipschitz embedding into some hyperbolic space X is Gromov hyperbolic and doubling up to some scale. In either case the image of the embedding is shown to be a Lipschitz retract in the target space, provided X is complete.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available