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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.