Characteristic points, rectifiability and perimeter measure on stratified groups
Valentino Magnani (2006)
Journal of the European Mathematical Society
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We establish an explicit connection between the perimeter measure of an open set with boundary and the spherical Hausdorff measure restricted to , when the ambient space is a stratified group endowed with a left invariant sub-Riemannian metric and denotes the Hausdorff dimension of the group. Our formula implies that the perimeter measure of is less than or equal to up to a dimensional factor. The validity of this estimate positively answers a conjecture raised by Danielli,...