A well known notion of k-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of Rk. 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,G)-approximate tangent group implies k-rectifiability.
Characterizations of k-rectifiability in homogeneous groups
Magnani, Valentino;Maiale, Francesco Paolo
2021
Abstract
A well known notion of k-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of Rk. 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,G)-approximate tangent group implies k-rectifiability.File in questo prodotto:
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