Calculus of Variations and Geometric Measure Theory
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K. O. Idu - F. P. Maiale

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

created by maiale on 19 Feb 2021



Inserted: 19 feb 2021

Year: 2021

ArXiv: 2102.05165 PDF


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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