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

Le Donne, Enrico; Rigot, Séverine

doi:10.1090/proc/12840

Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher
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by Enrico Le Donne and Séverine Rigot

Proc. Amer. Math. Soc. 144 (2016), 2003-2013

DOI: https://doi.org/10.1090/proc/12840

Published electronically: September 15, 2015

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Abstract:

We prove that the Besicovitch Covering Property (BCP) does not hold for some classes of homogeneous quasi-distances on Carnot groups of step 3 and higher. As a special case we get that, in Carnot groups of step 3 and higher, BCP is not satisfied for those homogeneous distances whose unit ball centered at the origin coincides with a Euclidean ball centered at the origin. This result comes in contrast with the case of the Heisenberg groups where such distances satisfy BCP.

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