Necessary conditions for length-minimality in sub-Riemannian geometry

Abstract

The regularity of length-minimizing curves on sub-Riemannian manifolds is a mystery. In this talk, I will discuss the metric blowup approach to the problem. The key ingredients are the iterative study of tangent cones of geodesics, and the cut-and-correct method to constructing competitors to potential length-minimizers. This talk is based on joint work with Enrico Le Donne.