Lipschitz and path isometric embeddings of metric spaces

Details Lipschitz and path isometric embeddings of metric spaces Lipschitz and path isometric embeddings of metric spaces

2010-05-10

arxiv.org/abs/1005.1623v1

Mathematics

Metric Geometry

Scientific paper

We prove that each sub-Riemannian manifold can be embedded in some Euclidean space preserving the length of all the curves in the manifold. The result is an extension of Nash C^1 Embedding Theorem. For more general metric spaces the same result is false, e.g., for Finsler non-Riemannian manifolds. However, we also show that any metric space of finite Hausdorff dimension can be embedded in some Euclidean space via a Lipschitz map.

Affiliated with

Also associated with

No associations

Rating

Lipschitz and path isometric embeddings of metric spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Lipschitz and path isometric embeddings of metric spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lipschitz and path isometric embeddings of metric spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-628768