Volume 21, Number 3, July-September 2015
|Page(s)||625 - 634|
|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
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
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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