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Author
Date
2010-05-10Type
- Working Paper
ETH Bibliography
yes
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Abstract
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. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversitySubject
Path isometry; Embedding; Sub-Riemannian manifold; Nash Embedding Theorem; Lipschitz embeddingOrganisational unit
03500 - Lang, Urs / Lang, Urs
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ETH Bibliography
yes
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