C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable
Differential Geometry
2007-05-23 v3 Metric Geometry
Abstract
We show that C^1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all C^1_H graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni for such surfaces.
Cite
@article{arxiv.math/0407223,
title = {C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable},
author = {Daniel R. Cole and Scott D. Pauls},
journal= {arXiv preprint arXiv:math/0407223},
year = {2007}
}
Comments
8 pages, new version adds expository material and context to introduction and simplifies one aspect of the proof of the main theorem