Geodesic
Corners in non-equiregular sub-Riemannian manifolds
Le Donne, Enrico1 ; Leonardi, Gian Paolo2 ; Monti, Roberto3 ; Vittone, Davide3 
1 University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35, 40014 Jyväskylä, Finland
2 Università di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, via Campi 213/b, 41100 Modena, Italy
3 Università di Padova, Dipartimento di Matematica, via Trieste 63, 35121 Padova, Italy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 625-634

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
DOI : 10.1051/cocv/2014041
Classification : 53C17, 49K21, 49J15
Keywords: Sub-Riemannian geometry, regularity of geodesics, corners

Le Donne, Enrico 1 ; Leonardi, Gian Paolo 2 ; Monti, Roberto 3 ; Vittone, Davide 3

1 University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35, 40014 Jyväskylä, Finland
2 Università di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, via Campi 213/b, 41100 Modena, Italy
3 Università di Padova, Dipartimento di Matematica, via Trieste 63, 35121 Padova, Italy 
@article{COCV_2015__21_3_625_0,
     author = {Le Donne, Enrico and Leonardi, Gian Paolo and Monti, Roberto and Vittone, Davide},
     title = {Corners in non-equiregular {sub-Riemannian} manifolds},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {625--634},
     publisher = {EDP-Sciences},
     volume = {21},
     number = {3},
     year = {2015},
     doi = {10.1051/cocv/2014041},
     mrnumber = {3358624},
     zbl = {1333.53045},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014041/}
}
TY  - JOUR
AU  - Le Donne, Enrico
AU  - Leonardi, Gian Paolo
AU  - Monti, Roberto
AU  - Vittone, Davide
TI  - Corners in non-equiregular sub-Riemannian manifolds
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2015
SP  - 625
EP  - 634
VL  - 21
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014041/
DO  - 10.1051/cocv/2014041
LA  - en
ID  - COCV_2015__21_3_625_0
ER  - 
%0 Journal Article
%A Le Donne, Enrico
%A Leonardi, Gian Paolo
%A Monti, Roberto
%A Vittone, Davide
%T Corners in non-equiregular sub-Riemannian manifolds
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2015
%P 625-634
%V 21
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2014041/
%R 10.1051/cocv/2014041
%G en
%F COCV_2015__21_3_625_0
Le Donne, Enrico; Leonardi, Gian Paolo; Monti, Roberto; Vittone, Davide. Corners in non-equiregular sub-Riemannian manifolds. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 3, pp. 625-634. doi: 10.1051/cocv/2014041

Cité par Sources :