Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher

DOI10.1090/proc/12840zbMath1361.53030arXiv1503.09034OpenAlexW1877494728WikidataQ109520633 ScholiaQ109520633MaRDI QIDQ2790917

Séverine Rigot, Enrico Le Donne

Publication date: 8 March 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.09034

zbMATH Keywords

Carnot groupscovering theoremsBesicovitch covering propertyhomogeneous quasi-distances

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Analysis on other specific Lie groups (43A80) Sub-Riemannian geometry (53C17) Set functions and measures on topological spaces (regularity of measures, etc.) (28C15)

Related Items (8)

Metric equivalences of Heintze groups and applications to classifications in low dimension ⋮ Besicovitch covering property for homogeneous distances on the Heisenberg groups ⋮ Periodic controls in step 2 strictly convex sub-Finsler problems ⋮ Differentiation of Measures in Metric Spaces ⋮ Blowups and blowdowns of geodesics in Carnot groups ⋮ Regularity properties of spheres in homogeneous groups ⋮ Coadjoint orbits and time-optimal problems for step-2 free nilpotent Lie groups ⋮ Besicovitch covering property on graded groups and applications to measure differentiation

Cites Work

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• Counter example to the Besicovitch covering property for some Carnot groups equipped with their Carnot-Carathéodory metric
• Lectures on analysis on metric spaces
• Foundations for the theory of quasiconformal mappings on the Heisenberg group
• Besicovitch covering property for homogeneous distances on the Heisenberg groups
• A smooth subadditive homogeneous norm on a homogeneous group
• Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces
• A general form of the covering principle and relative differentiation of additive functions
• A general form of the covering principle and relative differentiation of additive functions. II

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