The characteristic set of a surface
in the first Heisenberg group is the set of points where the surface is
tangent to the horizontal plane-field. In the first part of my talk I give
some sharp results on the size of this set in terms of the smoothness of
the surface. In the second part I apply these results to compare Hausdorff
measures with respect to the Heisenberg and the Euclidean metric.
|