Curvature-dimension condition of sub-Riemannian α-Grushin half-spaces

2024/09/17 by Samuël Borza, Borza, Samuël, Kenshiro Tashiro +1 · 1 citation
Mathematics · Physics and Astronomy · #49Q22 #53C17 #53C21 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Analysis and Transform Methods #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2409.11177

openalex publication_date 2024/09/17 · openalex created_date 2024/10/24 · openalex updated_date 2026/08/01

Abstract

We provide new examples of sub-Riemannian manifolds with boundary equipped with a smooth measure that satisfy the 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 α-Grushin plane.

Cited by

• Universal non-CD of sub-Riemannian manifolds

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• The Grushin hemisphere as a Ricci limit space with curvature ≥ 1
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• Half Space Property in RCD(K,N) spaces
• Almost-Riemannian manifolds do not satisfy the CD condition
• From almost smooth spaces to RCD spaces