2014/08/03 by Fabrice Baudoin, Baudoin, Fabrice, Bumsik Kim +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #Probability (math.PR) #math.AP #math.DG #math.PR
paper · pdf · doi:10.48550/arxiv.1408.0548
To be published in Communications in Analysis and Geometry
openalex publication_date 2014/08/03 · arxiv created 2015/10/14 · arxiv updated 2015/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a family of new Weitzenböck formulas on a Riemannian foliation with totally geodesic leaves. These Weitzenböck formulas are naturally parametrized by the canonical variation of the metric. As a consequence, under natural geometric conditions, the horizontal Laplacian satisfies a generalized curvature dimension inequality. Among other things, this curvature dimension inequality implies Li-Yau estimates for positive solutions of the horizontal heat equation and a sub-Riemannian Bonnet-Myers compactness theorem whose assumptions only rely on the intrinsic geometry of the horizontal distribution.