# Seminario di Equazioni Differenziali e Applicazioni: “Non-minimality of corners in subriemannian geometry”

## Martedì 24 Aprile 2018, ore 12:30 - Aula 2BC30 - Eero Hakavuori

ARGOMENTI: Seminari

Martedì 24 Aprile 2018 alle ore 12:30 in Aula 2BC30, Eero Hakavuori (Università di Jyaskyla) terrà un seminario dal titolo “Non-minimality of corners in subriemannian geometry”.

Abstract
The regularity of length-minimizing curves on subriemannian manifolds is an open problem, of which quite little is known outside of some specific cases. In the Riemannian setting, all length minimizers are solutions to a geodesic equation, which implies that all minimizers are smooth. The main difference in the subriemannian case is the existence of so called abnormal extremals, which do not satisfy any geodesic equation, but may nonetheless be minimizers. In this talk, I will outline a method used to prove that a piecewise $C^1$ length minimizer is necessarily everywhere $C^1$, that is, that curves with “corners” cannot be length-minimizing.
This talk is based on joint work with Enrico Le Donne.