Non-minimality of corners in subriemannian geometry

TL;DR

This paper proves that length minimizers in subriemannian geometry cannot have corner singularities, advancing the understanding of geodesic regularity and solving a long-standing open problem.

Contribution

It provides the first general proof that subriemannian geodesics are free of corner singularities, addressing a 30-year-old open problem.

Findings

Length minimizers have no corner-type singularities.

Solves Problem II of Agrachev's list.

Advances the regularity theory of subriemannian geodesics.

Abstract

We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.