Lipschitz and path isometric embeddings of metric spaces

被引：18
作者：
Le Donne, Enrico
机构：
来源：
GEOMETRIAE DEDICATA | 2013年 / 166卷 / 01期
关键词：
Path isometry; Embedding; Sub-Riemannian manifold; Nash embedding theorem; Lipschitz embedding;
D O I：
10.1007/s10711-012-9785-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：47 / 66
页数：20
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