{ "id": "1011.0365", "version": "v1", "published": "2010-11-01T16:19:56.000Z", "updated": "2010-11-01T16:19:56.000Z", "title": "Bi-Lipschitz Embeddability of the Grushin Plane into Euclidean Space", "authors": [ "Jeehyeon Seo" ], "comment": "13 pages", "categories": [ "math.MG" ], "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.", "revisions": [ { "version": "v1", "updated": "2010-11-01T16:19:56.000Z" } ], "analyses": { "subjects": [ "30L05", "53C17" ], "keywords": [ "euclidean space", "bi-lipschitz embeddability", "grushin plane admits", "whitney decomposition", "heisenberg group" ], "note": { "typesetting": "TeX", "pages": 13, "language": "en", "license": "arXiv", "status": "editable", "adsabs": "2010arXiv1011.0365S" } } }