Curvature‐dimension condition of sub‐Riemannian α$\alpha$‐Grushin half‐spaces

Abstract

We provide new examples of sub‐Riemannian manifolds with boundary equipped with a smooth measure that satisfy the $$\mathsf {RCD}(K, N)$$ condition. They are constructed by equipping the half‐plane, the hemisphere and the hyperbolic half‐plane with a two‐dimensional almost‐Riemannian structure and a measure that vanishes on their boundary. The construction of these spaces is inspired from the geometry of the $$\alpha$$‐Grushin plane.