Abstract: In a recent work Fässler, Le Donne, Ottazzi, Nicolussi Golo and Pansu proved that quasiconformal maps between non-compact geodesic Lie groups preserve the parabolic dimensions of the groups.
In this talk we first contextualize the previous result by presenting different strategies that show the non existence of quasiconformal maps between some 3D sub-Riemannian Lie groups. We shall examine later a preliminary study of rigidity between specific spaces where the parabolic dimension equals the Hausdorff dimension.
This is a work in progress with E. Le Donne, A. Tettamanti and J. Tyson.
