ON THE SUBANALYTICITY OF CARNOT-CARATHEODORY DISTANCES

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Genericity results for singular curves (2006, background): “Θs+1 = det  ( h [1] ij ) 16i6m−1 16j6m ( L−→ h j Θs ) 16j6m  , Θ0 = det  ( h [1] ij ) 16i6m−1 16j6m ( h [2] 1j ) 16j6m  ,”
Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “The heat kernel on sub-Riemannian manifolds has been an object of attention starting from the late 70s [14, 16, 17, 19, 21, 26, 32, 38, 41, 54, 55], as have the geodesics and cut and conjugate loci of such manifolds [6, 7, 2, 11, 3, 25, 29, 43, 52].”
Optimal transportation under nonholonomic constraints (2007, background): “In particular, it is proved in [3] that a generic distribution of rank > 2 does not admit nonconstant sharp trajectories.”
On the Hausdorff volume in sub-Riemannian geometry (2010, unknown): “In the case in which {ρt}t>0 is the approximating family of the nilpotent distance ρ̂, this result is proved in [3].”