Abstract
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In this paper, we show that the flatness of tangents of
-codimensional measures in Carnot
groups implies
-rectifiability.
As applications we prove a criterion for intrinsic Lipschitz rectifiability of finite
perimeter sets in general Carnot groups and we show that measures with
-density in the
Heisenberg groups
are
-rectifiable,
providing the first non-Euclidean extension of Preiss’s rectifiability theorem.
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Keywords
Marstrand–Mattila rectifiability criterion, Preiss's
rectifiability theorem, Carnot groups
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Mathematical Subject Classification
Primary: 28A75, 53C17
Secondary: 22E25, 49Q15
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Milestones
Received: 16 December 2020
Revised: 14 September 2021
Accepted: 28 October 2021
Published: 15 June 2023
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| © 2023 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
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