Mathematische Zeitschrift

, Volume 282, Issue 1–2, pp 99–130 | Cite as

Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part I

  • Erlend GrongEmail author
  • Anton Thalmaier


We give a generalized curvature-dimension inequality connecting the geometry of sub-Riemannian manifolds with the properties of its sub-Laplacian. This inequality is valid on a large class of sub-Riemannian manifolds obtained from Riemannian foliations. We give a geometric interpretation of the invariants involved in the inequality. Using this inequality, we obtain a lower bound for the eigenvalues of the sub-Laplacian. This inequality also lays the foundation for proving several powerful results in Part II.


Curvature-dimension inequality Sub-Riemannian geometry Hypoelliptic operator Spectral gap Riemannian foliations 

Mathematics Subject Classification

58J35 53C17 58J99 



This work has been supported by the Fonds National de la Recherche Luxembourg (AFR 4736116 and OPEN Project GEOMREV).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Mathematics Research Unit, FSTCUniversity of LuxembourgLuxembourgGrand Duchy of Luxembourg

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