Geometry, Topology and Dynamics Seminar
Severine Rigot
Universite de Nice Sophia Antipolis
Isodiametric inequality in Carnot-Caratheodory spaces
Abstract: Carnot-Caratheodory structures, also known as Sub-Riemannian structures, arise naturally in many situations.
They arise for example as limits of certain Riemannian metrics on some nilpotent Lie groups.
It is now well-known that the geometry induced by these Carnot-Cartheodory structures can be in many ways extremely different
from that of Riemannian spaces. We will illustrate this phenomenon showing how classical geometrical properties of
the Euclidean space, such as the isodiametric inequality, can fail to hold and giving some consequences of these facts.
This work is mainly based on the study of specific features of the distance function and of minimal curves.
Monday April 20, 2009 at 3:00 PM in SEO 612