Abstract
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].
| Original language | English |
|---|---|
| Pages (from-to) | 1177-1203 |
| Number of pages | 27 |
| Journal | Mathematical Research Letters |
| Volume | 24 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2017 |
Keywords
- Bi-Lipschitz embedding
- Generalized Grushin plane
- Quasiplane
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