Yu. L. Sachkov, “Complete description of the Maxwell strata in the generalized Dido problem”, Sbornik: Mathematics, 2006, 197:6, 901–950
The generalized Dido problem is considered — a model of the nilpotent sub-Riemannian problem with the growth vector (2, 3, 5). The Maxwell set is studied, that is, the locus of the intersection points of geodesics of equal length. A complete description is obtained for the Maxwell strata corresponding to the symmetry group of the exponential map generated by rotations and reflections. All the corresponding Maxwell times are found and located. The conjugate points that are limit points of the Maxwell set are also found. An upper estimate is obtained for the cut time (time of loss of optimality) on geodesics.