| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 75 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/cocv/2022074 | |
| Published online | 22 December 2022 | |
The Sard problem in step 2 and in filiform Carnot groups*,,**
1
Dipartimento di Matematica “T. Levi-Civita”,
via Trieste 63,
35121
Padova,
Italy
2
Département de Mathématiques,
Ch. du musée 23,
1700
Fribourg (CH)
*** Corresponding author: davide.vittone@unipd.it
Received:
1
April
2022
Accepted:
6
November
2022
We study the Sard problem for the endpoint map in some well-known classes of Carnot groups. Our first main result deals with step 2 Carnot groups, where we provide lower bounds (depending only on the algebra of the group) on the codimension of the abnormal set; it turns out that our bound is always at least 3, which improves the result proved in Le Donne et al. [Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016) 1639–1666] and settles a question emerged in Ottazzi and Vittone [ESAIM: COCV 25 (2019) 18]. In our second main result we characterize the abnormal set in filiform groups and show that it is either a horizontal line, or a 3-dimensional algebraic variety.
Mathematics Subject Classification: 53C17 / 58K05 / 22E25
Key words: Sard problem / Carnot groups / abnormal curves
© The authors. Published by EDP Sciences, SMAI 2022
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