| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 18 | |
| Number of page(s) | 17 | |
| DOI | https://doi.org/10.1051/cocv/2018002 | |
| Published online | 18 July 2019 | |
On the codimension of the abnormal set in step two Carnot groups★,★★
1
School of Mathematics and Statistics, UNSW Kensington Campus,
Sydney,
NSW 2052, Australia
2
Dipartimento di Matematica,
via Trieste 63,
35121
Padova, Italy
*** Corresponding author: a.ottazzi@unsw.edu.au
Received:
2
November
2017
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
© EDP Sciences, SMAI 2019
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