Illinois Journal of Mathematics

Geometry of Grushin spaces

Jang-Mei Wu

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We compare the Grushin geometry to Euclidean geometry, through quasisymmetric parametrization, bilipschitz parametrization and bilipschitz embedding, highlighting the role of the exponents and the fractal nature of the singular hyperplanes in Grushin geometry.

Article information

Illinois J. Math., Volume 59, Number 1 (2015), 21-41.

Received: 31 October 2014
Revised: 16 January 2015
First available in Project Euclid: 11 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C17: Sub-Riemannian geometry
Secondary: 30L05: Geometric embeddings of metric spaces


Wu, Jang-Mei. Geometry of Grushin spaces. Illinois J. Math. 59 (2015), no. 1, 21--41. doi:10.1215/ijm/1455203157.

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