Calculus of Variations and Geometric Measure Theory

E. Le Donne - E. Hakavuori

Non-minimality of corners in subriemannian geometry

created by ledonne on 29 Mar 2016


Accepted Paper

Inserted: 29 mar 2016
Last Updated: 29 mar 2016

Journal: Inventiones Math.
Pages: 11
Year: 2016


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.

Keywords: Carnot groups, sub-Riemannian geometry, Geodesics, Corner-type singularities, regularity of length minimizers