Calculus of Variations and Geometric Measure Theory

V. Magnani

A new differentiation, shape of the unit ball and perimeter measure

created by magnani on 10 Sep 2014
modified on 12 Jun 2017


Published Paper

Inserted: 10 sep 2014
Last Updated: 12 jun 2017

Journal: Indiana Univ. Math. J.
Volume: 66
Number: 1
Pages: 183-204
Year: 2017


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.

Tags: GeMeThNES
Keywords: Carnot group, perimeter measure, stratified group, spherical Hausdorff measure