S.Rigot - Besicovitch covering property in sub-Riemannian geometry

Séverine Rigot (1) , Fanny Bastien (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IF - Institut Fourier

The Besicovitch covering property originates from works of Besicovitch about differentiation of measures in Euclidean spaces. It can more generally be used as a usefull tool to deduce global properties of a metric space from local ones. We will discuss in this talk the validity or non validity of the Besicovitch covering property on stratified groups equipped with sub Riemannian distances (Carnot groups) and more generally on graded groups equipped with homogeneous distances. We will illustrate these results with explicit examples in the Heisenberg group. We will also discuss some consequences related to the theory of differentiation of measures on sub-Riemannian manifolds. Based on joint works with E. Le Donne and S. Nicolussi Golo.

Mots clés: sub-riemannian days 2017; sub-riemannian; besicovitch covering property; geometry

Mots clés: sous-riemannien; grenoble; journées sous-riemanniennes 2017

Domaines: Mathématiques [math]

Séverine Rigot, Fanny Bastien. S.Rigot - Besicovitch covering property in sub-Riemannian geometry: Sub-riemannian days 2017. 2017. ⟨medihal-01721741⟩