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Bi-Lipschitz embedding of the generalized Grushin plane in Euclidean spaces by Romney, Matthew; Vellis, Vyron is a scholarly article available to read on EtoBox.

What is Bi-Lipschitz embedding of the generalized Grushin plane in Euclidean spaces about?

We show that, for all $\alpha\geq 0$, the generalized Grushin plane $\mathbb{G}_{\alpha}$ is bi-Lipschitz homeomorphic to a $2$-dimensional quasiplane in the Euclidean space $\mathbb{R}^{[\alpha ]+2}$, where $[\alpha]$ is the integer part of $\alpha$. The target dimension is sharp. This generalizes a recent result of Wu.

Author

Romney, Matthew; Vellis, Vyron

Published

2015

Language

EN