Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations

@article{Baudoin2017SubLaplacianCT,
  title={Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations},
  author={Fabrice Baudoin and E. Grong and Kazumasa Kuwada and Anton Thalmaier},
  journal={arXiv: Differential Geometry},
  year={2017}
}
We develop a variational theory of geodesics for the canonical variation of the metric of a totally geodesic foliation. As a consequence, we obtain comparison theorems for the horizontal and vertical Laplacians. In the case of Sasakian foliations, we show that sharp horizontal and vertical comparison theorems for the sub-Riemannian distance may be obtained as a limit of horizontal and vertical comparison theorems for the Riemannian distances approximations. 
Comparison theorems on H-type sub-Riemannian manifolds
Harnack inequalities on totally geodesic foliations with transverse Ricci flow
Affine connections and curvature in sub-Riemannian geometry
Radial processes for sub-Riemannian Brownian motions and applications
H-type foliations
Left-invariant geometries on SU(2) are uniformly doubling
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References

SHOWING 1-10 OF 48 REFERENCES
Sub-Laplacians and hypoelliptic operators on totally geodesic Riemannian foliations
Stochastic analysis on sub-Riemannian manifolds with transverse symmetries
Sub-Riemannian Curvature in Contact Geometry
Variational problems on contact Riemannian manifolds
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part I
Any sub-Riemannian metric has points of smoothness
Bishop and Laplacian comparison theorems on Sasakian manifolds
Curvature-dimension inequalities on sub-Riemannian manifolds obtained from Riemannian foliations: part II
On the measure contraction property of metric measure spaces
...
1
2
3
4
5
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