On the cut locus of free, step two Carnot groups


In this note, we study the cut locus of the free, step two Carnot groups Gk with k generators, equipped with their left-invariant Carnot-Carathéodory metric. In particular, we disprove the conjectures on the shape of the cut loci proposed in [Mya02, Mya06] and [MM16a], by exhibiting sets of cut points Ck ⊂ Gk which, for k > 4, are strictly larger than… (More)