标题： 子黎曼$α$-Grushin 半空间的曲率-维数条件 显示英文标题

标题： Curvature-dimension condition of sub-Riemannian $α$-Grushin half-spaces

摘要： 我们提供了带有边界的新子黎曼流形示例，这些流形配备了满足$\mathsf{RCD}(K , N)$条件的光滑测度。 它们是通过将半平面、半球和双曲半平面赋予二维几乎黎曼结构以及在其边界上消失的测度来构造的。 这些空间的构造受到$\alpha$-Grushin 平面几何的启发。 显示英文摘要

摘要： 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.