Excess and tangents of sub-Riemannian geodesics

geodesics
Grenoble
[MATH]Mathematics [math]
sub-riemannian
sous-riemannien
sub-riemannian days 2017
journées sous-riemanniennes 2017
excess
tangents

Appears in collection : Journée sous-riemannienne 2017

We present some recent results on the regularity problem of sub-Riemannian length minimizing curves. This is a joint work with A. Pigati and D. Vittone. After introducing the notion of excess for a horizontal curve, we show that at any point of a length minimizing curve excess is infinitesimal at some sequence of scales. This implies the existence of a linear tangent. We also discuss other results related to excess.