The regularity problem for geodesics of the control distance

Abstract

In this survey, we present some recent results on the problem about the regularity of length-minimizing curves in sub-Riemannian geometry. We also sketch the possible application of some ideas coming from Geometric Measure Theory.

Keywords

• geodesics
• regularity of length minimizers
• carnot-carathéodory spaces
• sub-riemannian geometry
• carnot groups