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

Characterizations of $k$-rectifiability in homogenous groups

created by magnani on 10 Sep 2020
modified on 18 Sep 2020

[BibTeX]

Submitted Paper

Inserted: 10 sep 2020
Last Updated: 18 sep 2020

Year: 2020
Links: ArXiv

Abstract:

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


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