6533b821fe1ef96bd127c1f0

RESEARCH PRODUCT

Corners in non-equiregular sub-Riemannian manifolds

Davide VittoneGian Paolo LeonardiRoberto MontiEnrico Le Donne

subject

Mathematics - Differential GeometryPure mathematicsClass (set theory)Control and Optimizationregularity of geodesicsStructure (category theory)Mathematics - Analysis of PDEsMathematics - Metric GeometryFOS: MathematicsGEOMSub-Riemannian geometry regularity of geodesics cornersMathematics - Optimization and ControlMathematicsta111Computational mathematicsMetric Geometry (math.MG)cornerssub-riemannian geometryComputational MathematicsCorners; Regularity of geodesics; Sub-Riemannian geometry; Control and Systems Engineering; Control and Optimization; Computational MathematicsDifferential Geometry (math.DG)Mathematics Subject ClassificationOptimization and Control (math.OC)Control and Systems EngineeringMathematics::Differential GeometryAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2014-03-10
http://arxiv.org/abs/1403.2356