Calculus of Variations and Geometric Measure Theory

K. O. Idu - V. Magnani - F. P. Maiale

Characterizations of $k$-rectifiability in homogenous groups

created by magnani on 10 Sep 2020
modified on 13 May 2021


Published Paper

Inserted: 10 sep 2020
Last Updated: 13 may 2021

Journal: J. Math. Anal. Appl.
Volume: 500
Number: 2
Pages: 20
Year: 2021
Links: ArXiv


A well known notion of $k$-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of $\mathbb{R}^k$. We prove some characterizations of $k$-rectifiability, when the metric space is an arbitrary homogeneous group. In particular, we show that the a.e. existence of the $(k,\mathbb{G})$-approximate tangent group implies $k$-rectifiability.

Keywords: homogeneous group, approximate tangent group, rectifiability, Lipschitz mapping