arXiv:1011.0365 Abstract | arXiv Analytics

arXiv:1011.0365 [math.MG]Abstract References Reviews Resources

Bi-Lipschitz Embeddability of the Grushin Plane into Euclidean Space

Published 2010-11-01Version 1

Many sub-Riemannian manifolds like the Heisenberg group do not admit bi- Lipschitz embedding into any Euclidean space. In contrast, the Grushin plane admits a bi-Lipschitz embedding into some Euclidean space. This is done by extending a bi-Lipschitz embedding of the singular line, using a Whitney decomposition of its complement.

Comments: 13 pages

Categories: math.MG

Subjects: 30L05, 53C17

Keywords: euclidean space, bi-lipschitz embeddability, grushin plane admits, whitney decomposition, heisenberg group

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