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

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 $0 < \alpha \leq 1$. 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.Comment: Corrected typos. Added more information in Section 2.1 (preliminaries) and detailed proofs in Section 2.2. Added Lemma 3.3 and modified the main proof (Section 3.1) accordingl