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Friday, September 11, 2015

**Abstract:** The classical Grushin plane is a standard example of a sub-Riemannian manifold. It is known to be quasisymmetrically homeomorphic to the standard Euclidean plane, and to admit a bi-Lipschitz embedding in Euclidean 3-space. In this talk we will introduce a more general class of surfaces modeled on the Grushin plane. We prove that, under suitable assumptions, they can be embedded in some Euclidean space under a bi-Lipschitz map. Finally, we will discuss possibilities for further research.