Remarks about the Besicovitch Covering Property in Carnot groups of step 3 and higher
Authors:
Enrico Le Donne and Séverine Rigot
Journal:
Proc. Amer. Math. Soc. 144 (2016), 2003-2013
MSC (2010):
Primary 28C15, 49Q15, 43A80
DOI:
https://doi.org/10.1090/proc/12840
Published electronically:
September 15, 2015
MathSciNet review:
3460162
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Enrico Le Donne
Affiliation:
Department of Mathematics and Statistics, P.O. Box 35, FI-40014, University of Jyväskylä, Finland
Email:
ledonne@msri.org
Séverine Rigot
Affiliation:
Laboratoire de Mathématiques J.A. Dieudonné UMR CNRS 7351, Université Nice Sophia Antipolis, 06108 Nice Cedex 02, France
Email:
rigot@unice.fr
DOI:
https://doi.org/10.1090/proc/12840
Keywords:
Covering theorems,
Carnot groups,
homogeneous quasi-distances
Received by editor(s):
April 8, 2015
Received by editor(s) in revised form:
May 18, 2015
Published electronically:
September 15, 2015
Additional Notes:
The work of the second author was supported by the ANR-12-BS01-0014-01 Geometrya.
Communicated by:
Jeremy Tyson
Article copyright:
© Copyright 2015
American Mathematical Society