Abstract or Additional Information
An important problem in Sub-Riemannian geometry is the isoperimetric problem. In the euclidean case, the Brunn-Minkowski inequality provides a direct proof of an optimal isoperimetric inequality and characterize the euclidean balls as the only isoperimetric regions.
In this talk we shall extend the proof of Hadwiger and Ohman of the Brunn-Minkowski inequality to Nilpotent Lie groups and verify that the inequality is strict even for simple cases. We will provide several equivalent statements, emphasizing the case of Carnot groups.