Corners in non-equiregular sub-Riemannian manifolds

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. P...

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Published inESAIM. Control, optimisation and calculus of variations Vol. 21; no. 3; pp. 625 - 634
Main Authors Le Donne, Enrico, Leonardi, Gian Paolo, Monti, Roberto, Vittone, Davide
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.07.2015
Subjects
49J15
49K21
53C17
Corners
regularity of geodesics
Riemann manifold
Sub-Riemannian geometry
Theorems
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Summary: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.
Bibliography:publisher-ID:cocv140041
PII:S1292811914000414
ark:/67375/80W-JZHK1HNF-N
istex:92FC0091063B9F2496843D4C46E10BB888440E9E
ledonne@msri.org
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2014041