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arXiv · 2102.05165

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

Kennedy Obinna Idu·Francesco Paolo Maiale
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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 $0 < \alpha \leq 1$. 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.

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Kennedy Obinna Idu, Francesco Paolo Maiale. 2021-02-09. $C^{1,\alpha}$-rectifiability in low codimension in Heisenberg groups. https://doi.org/10.1515/agms-2023-0105

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