Equivalence of Strong Brunn-Minkowski Inequalities and CD Conditions in Heisenberg Groups

2023/06/09 by Juan Zhang, Zhang, Juan, Peibiao Zhao +1
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2306.05650

openalex publication_date 2023/06/09 · openalex created_date 2023/06/13 · openalex updated_date 2026/07/28

Abstract

The present paper investigates the sub-Riemannian version of the equivalence between the curvature-dimension conditions and strong Brunn-Minkowski inequalities in the sub-Riemannian Heisenberg group Hn. We adopt the optimal transport and approximation of Hn developed by Ambrosio and Rigot [1] and combine the celebrated works by M. Magnabosco, L. Portinale and T. Rossi [17] to confirm this.

Related

• Geometric inequalities on Heisenberg groups
• The Minkowski problem in Heisenberg groups
• Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups
• The Brunn--Minkowski inequality implies the CD condition in weighted Riemannian manifolds
• Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group