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

Communications on Pure &amp Applied Analysis 2026 Open access

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Authors: Fabrice Baudoin
DOI: 10.3934/cpaa.2026035
Cited by: 0
References: 12

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 allows 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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Spectral Theory in Mathematical Physics

Publication details

Journal / source
Communications on Pure &amp Applied Analysis
Volume
32
Issue
0
Pages
192–214
Publication date
1 January 2026
Language
EN