Illinois Journal of Mathematics

Geometry of Grushin spaces

Jang-Mei Wu

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1455203157

Digital Object Identifier
doi:10.1215/ijm/1455203157

Mathematical Reviews number (MathSciNet)
MR3459626

Zentralblatt MATH identifier
1339.53030

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

Citation

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


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