Nilpotent (3, 6) Sub-Riemannian Problem

By O. Myasnichenko. 2002

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Small time heat kernel asymptotics at the sub-Riemannian cut locus (2012, background): “These facts were proved in [46] with a detailed analysis of the exponential map.”
On the cut locus of free, step two Carnot groups (2016, background): “ts(0,Y) ∈R2 ⊕∧2R2,withY 6= 0 . Thecomputationofthecuttimeandcutlocusfor thecasek= 3 ismuchharder,andrequiresacarefulmanipulationofgeodesicequations and symmetries. This has been done independently in [Mya02] and [MM16a]. There, it wasprovedthat,forthestep2 freeCarnotgroupsofrankk= 2,3,onehas (15) Cu”
Control theory on lie groups (2009, background): “(3) papers on optimal control for invariant problems on Lie groups [10, 23, 24, 25, 26, 29 , 36, 37],”
On the subRiemannian cut locus in a model of free two-step Carnot group (2016, methodology): “eferences 26 Abstract We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators, giving a new, independent proof of a result by Myasnichenko [Mya02]. We also calculate explicitly the cut time of any extremal path and the distance from the or”