Calculus of Variations and Geometric Measure Theory

S. Borza

Distortion Coefficients of the $\alpha$-Grushin Plane

created by borza on 13 Jan 2022


Published Paper

Inserted: 13 jan 2022
Last Updated: 13 jan 2022

Journal: The Journal of Geometric Analysis
Volume: 32
Number: Issue 3
Pages: Article 78
Year: 2022
Doi: 10.1007/s12220-021-00736-8

ArXiv: 2010.16350 PDF


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