ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Daniel Cole (Dartmouth College)
N-Rectifiability in the Heisenberg Group

Abstract: We say that a subset E of a Carnot group M is countably N-rectifiable if, up to Hausdorff measure, it is the countable union of Lipschitz images of a subgroup N of another Carnot group. In this talk, we prove that C¹ hypersurfaces of the three dimensional Heisenberg Group are N-rectifiable, where N is a subgroup of of co-dimension one. In this context, N-rectifiability retains much of the flavor of Euclidean rectifiability in that N-rectifiable sets look locally like their tangent approximations.