Lipschitz and path isometric embeddings of metric spaces View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-10

AUTHORS

Enrico Le Donne

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 C1 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. More... »

PAGES

47-66

References to SciGraph publications

Journal

TITLE

Geometriae Dedicata

ISSUE

1

VOLUME

166

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10711-012-9785-2

DOI

http://dx.doi.org/10.1007/s10711-012-9785-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1006006420


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