Corners in non-equiregular sub-Riemannian manifolds

2014/03/10 by Donne, Enrico Le, Leonardi, Gian Paolo, Monti, Roberto +1
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1403.2356

Abstract

We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results [4]. As an application of our main result we complete and simplify the analysis in [6], showing that in a 4-dimensional sub-Riemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth.

Related

• Sharp regularity of sub-Riemannian length-minimizing curves
• Not all sub-Riemannian minimizing geodesics are smooth
• On manifolds with corners
• Manifolds with analytic corners
• Nonminimality of spirals in sub-Riemannian manifolds