Calculus of Variations and Geometric Measure Theory
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E. Le Donne - S. Rigot

Remarks about Besicovitch covering property in Carnot groups of step 3 and higher

created by ledonne on 21 Dec 2018



Inserted: 21 dec 2018

Year: 2015

ArXiv: 1503.09034 PDF


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 constrast with the case of the Heisenberg groups where such distances satisfy BCP.

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