Measure of curves in graded groups

Abstract

We consider continuously differentiable curves embedded in graded groups, along with the points of these curves that have the maximal transversality with respect to the grading of the group. We prove a blow-up theorem at these points and we show that the remaining points are negligible with respect to the Hausdorff measure whose dimension equals the Hausdorff dimension of the curve. This leads us to an area-type formula for the intrinsic spherical Hausdorff measure of any of these curves embedded in an arbitrary graded group.