arXiv 1503.090342015-03-31math.MG

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

Enrico Le Donne, Severine Rigot

英文摘要：

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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