Bi-Lipschitz Embeddability of the Grushin Plane into Euclidean Space
arXiv:1011.0365
Abstract
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.
13 pages