C^1 Hypersurfaces of the Heisenberg Group are N-Rectifiable

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.

arXiv comment8 pages, new version adds expository material and context to introduction and simplifies one aspect of the proof of the main theorem

Cited by in corpus (2)

• Rickman rugs and intrinsic bilipschitz graphs
• Rectifiability; a survey