Distortion coefficients of the $\alpha$-Grushin plane

Abstract

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 synthetic curvature condition for the generalised Grushin planes is suggested.

27 pages, 2 figures. v2: typos corrected; acknowledgments, keywords and MSC class added. v3: correction to (12) which simplifies some equations; Final version to appear in The Journal of Geometric Analysis

References in corpus (3)

• Sub-Riemannian interpolation inequalities
• A counterexample to gluing theorems for MCP metric measure spaces
• SubRiemanniann structures do not satisify Riemannian Brunn--Minkowski inequalities