A new differentiation, shape of the unit ball and perimeter measure
  We present a new blow-up method that allows for establishing the first general formula to compute the perimeter measure with respect to the spherical Hausdorff measure in noncommutative nilpotent groups. This result leads us to an unexpected relationship between the area formula with respect to a distance and the profile of its corresponding unit ball. 
Valentino Magnani
math.DG math.FA math.MG