Sub-Laplacian comparison theorems on Riemannian foliations with minimal leaves and applications

2025/09/16 by Fabrice Baudoin, Baudoin, Fabrice
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2509.13276

openalex publication_date 2025/09/16 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We prove comparison theorems for the horizontal Laplacian of the Riemannian distance in the context of Riemannian foliations with minimal leaves. This general framework generalizes previous works and allow us to consider the sub-Laplacian of Carnot groups of arbitrary steps. The comparison theorems yield a Bonnet-Myers type theorem, stochastic completeness and Lipschitz regularization property for the sub-Riemannian semigroup.

Citations

• Topology and bottom spectrum of transversally negatively curved foliations
• Radial processes for sub-Riemannian Brownian motions and applications
• Exponential integrability and exit times of diffusions on sub-Riemannian\n and metric measure spaces
• Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
• Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations
• Stochastic analysis on sub-Riemannian manifolds with transverse\n symmetries
• Curvature-dimension inequalities and Ricci lower bounds for\n sub-Riemannian manifolds with transverse symmetries
• Connections and Curvature in sub-Riemannian geometry

Related

• Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
• Comparison principle, stochastic completeness and half-space theorems
• Sub-Laplacians on sub-Riemannian manifolds
• Radial processes for sub-Riemannian Brownian motions and applications
• Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations