Inserted: 13 jan 2022
Last Updated: 13 jan 2022
Journal: The Journal of Geometric Analysis
Number: Issue 3
Pages: Article 78
We compute the distortion coefficients of the $\alpha$-Grushin plane. They are expressed in terms of generalised trigonometric functions. Estimates for the distortion coefficients are then obtained and a conjecture of a measure contraction property condition for the generalised Grushin planes is suggested.
Keywords: sub-Riemannian geometry, Grushin plane, Distortion coefficients, Synthetic curvature