30 mar 2006

Abstract.

Séverine Rigot, from Département de Mathématiques d'Orsay, Université Paris-Sud

on Thursday, 30 March, in ``Sala dei Seminari'' of the Mathematics Department

at 17:30, will hold a seminar on

Remarks about minimal curves in Carnot groups

ABSTRACT: It is well-known that Riemannian and sub-Riemannian geometry can be extremely different. This can be for instance reflected through differentiability, or non differentiability, properties of the distance function and qualitative behaviour of minimal curves. We will try to illustrate this phenomenon. We will show how classical geometrical properties of Euclidean spaces, namely the Besicovitch covering property and the isodiametric inequality, can fail to hold in Carnot groups, counter-examples being based on specific features of the distance function and minimal curves.