On the codimension of the abnormal set in step two Carnot groups
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 18.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2018002
Classification : 53C17, 22E25, 14M17
Mots-clés : Sard property, endpoint map, abnormal curves, Carnot groups, sub-Riemannian geometry
Ottazzi, Alessandro 1 ; Vittone, Davide 1

1 
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     title = {On the codimension of the abnormal set in step two {Carnot} groups},
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Ottazzi, Alessandro; Vittone, Davide. On the codimension of the abnormal set in step two Carnot groups. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 18. doi : 10.1051/cocv/2018002. http://www.numdam.org/articles/10.1051/cocv/2018002/

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