Calculus of Variations and Geometric Measure Theory

A. Merlo

Marstrand-Mattila rectifiability criterion for $1$-codimensional measures in Carnot Groups

created by merlo on 29 Sep 2020
modified on 31 Dec 2021


Accepted Paper

Inserted: 29 sep 2020
Last Updated: 31 dec 2021

Journal: Analysis & PDE
Year: 2020

ArXiv: 2007.03236 PDF


This paper is devoted to show that the flatness of tangents of $1$-codimensional measures in Carnot Groups implies $C^1_\mathbb{G}$-rectifiability. As applications we prove that measures with $(2n+1)$-density in the Heisenberg groups $\mathbb{H}^n$ are $C^1_{\mathbb{H}^n}$-rectifiable, providing the first non-Euclidean extension of Preiss's rectifiability theorem and a criterion for intrinsic Lipschitz rectifiability of finite perimeter sets in general Carnot groups.