TY - JOUR
T1 - Bi-Lipschitz embedding of the generalized Grushin plane into Euclidean spaces
AU - Romney, Matthew
AU - Vellis, Vyron
PY - 2017
Y1 - 2017
N2 - We show that, for all α ≥ 0, the generalized Grushin plane Gα is bi-Lipschitz homeomorphic to a 2-dimensional quasiplane in the Euclidean space R⌊α⌋+2, where ⌊α⌋ is the integer part of α. The target dimension is sharp. This generalizes a recent result of Wu [22].
AB - We show that, for all α ≥ 0, the generalized Grushin plane Gα is bi-Lipschitz homeomorphic to a 2-dimensional quasiplane in the Euclidean space R⌊α⌋+2, where ⌊α⌋ is the integer part of α. The target dimension is sharp. This generalizes a recent result of Wu [22].
KW - Bi-Lipschitz embedding
KW - Generalized Grushin plane
KW - Quasiplane
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U2 - 10.4310/MRL.2017.v24.n4.a11
DO - 10.4310/MRL.2017.v24.n4.a11
M3 - Article
AN - SCOPUS:85033369343
SN - 1073-2780
VL - 24
SP - 1177
EP - 1203
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 4
ER -