| Issue |
ESAIM: COCV
Volume 21, Number 3, July-September 2015
|
|
|---|---|---|
| Page(s) | 625 - 634 | |
| DOI | https://doi.org/10.1051/cocv/2014041 | |
| Published online | 01 May 2015 | |
Corners in non-equiregular sub-Riemannian manifolds
1 University of Jyväskylä, Department
of Mathematics and Statistics, P.O. Box 35, 40014
Jyväskylä,
Finland
ledonne@msri.org
2 Università di Modena e Reggio Emilia,
Dipartimento di Scienze Fisiche, Informatiche e Matematiche,
via Campi 213/b, 41100
Modena, Italy
gianpaolo.leonardi@unimore.it
3 Università di Padova, Dipartimento di
Matematica, via Trieste
63, 35121
Padova,
Italy
monti@math.unipd.it; vittone@math.unipd.it
Received:
10
March
2014
We prove that in a class of non-equiregular sub-Riemannian manifolds corners are not length minimizing. This extends the results of [G.P. Leonardi and R. Monti, Geom. Funct. Anal. 18 (2008) 552–582]. As an application of our main result we complete and simplify the analysis in [R. Monti, Ann. Mat. Pura Appl. (2013)], showing that in a 4-dimensional sub-Riemannian structure suggested by Agrachev and Gauthier all length-minimizing curves are smooth.
Mathematics Subject Classification: 53C17 / 49K21 / 49J15
Key words: Sub-Riemannian geometry / regularity of geodesics / corners
© EDP Sciences, SMAI 2015
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