Volume 25, 2019
|Number of page(s)||17|
|Published online||18 July 2019|
School of Mathematics and Statistics, UNSW Kensington Campus,
NSW 2052, Australia
2 Dipartimento di Matematica, via Trieste 63, 35121 Padova, Italy
*** Corresponding author: email@example.com
Accepted: 10 January 2018
In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three. Our result applies to all step 2 Carnot groups of dimension up to 7 and is a generalisation of a previous analogous result for step 2 free nilpotent groups.
Mathematics Subject Classification: 53C17 / 22E25 / 14M17
Key words: Sard property / endpoint map / abnormal curves / Carnot groups / sub-Riemannian geometry
D.V. is supported by University of Padova, Project Networking, and GNAMPA of INdAM (Italy), project Campi vettoriali, superfici e perimetri in geometrie singolari.
© EDP Sciences, SMAI 2019
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