$C^{1,\alpha }$-rectifiability in low codimension in Heisenberg groups

Abstract

A natural notion of higher order rectifiability is introduced for subsets of Heisenberg groups ${\mathbb{H}}^n$ in terms of covering a set almost everywhere by a countable union of $({\mathbf{C}}_H^{1,\alpha },\mathbb{H})$-regular surfaces, for some $0<\alpha \le 1$. We prove that a sufficient condition for $C^{1,\alpha }$-rectifiability of low-codimensional subsets in Heisenberg groups is the almost everywhere existence of suitable approximate tangent paraboloids.

Corrected typos and general improvements to the proofs

References in corpus (1)

• Rectifiability and approximate differentiability of higher order for sets