Calculus of Variations and Geometric Measure Theory

K. O. Idu - F. P. Maiale

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

created by maiale on 19 Feb 2021
modified on 06 Sep 2023



Inserted: 19 feb 2021
Last Updated: 6 sep 2023

Year: 2023

ArXiv: 2102.05165v3 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.