0000000000958311

AUTHOR

Zeinab Badreddine

showing 2 related works from this author

Mass transportation on sub-Riemannian structures of rank two in dimension four

2017

International audience; This paper is concerned with the study of the Monge optimal transport problem in sub-Riemannian manifolds where the cost is given by the square of the sub-Riemannian distance. Our aim is to extend previous results on existence and uniqueness of optimal transport maps to cases of sub-Riemannian structures which admit many singular minimizing geodesics. We treat here the case of sub-Riemannian structures of rank two in dimension four.

Mathematics - Differential Geometry[ MATH ] Mathematics [math]Rank (linear algebra)Geodesicpolar factorization[MATH] Mathematics [math]01 natural sciencesSquare (algebra)CombinatoricsDimension (vector space)0103 physical sciencesFOS: MathematicsUniqueness0101 mathematicsMass transportation[MATH]Mathematics [math]Mathematical PhysicsComputingMilieux_MISCELLANEOUSMathematicsApplied Mathematics010102 general mathematicsSub-Riemannian geometryDifferential Geometry (math.DG)[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]010307 mathematical physicsMathematics::Differential GeometryAnalysisOptimal transport problem
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Transport optimal sur les structures sous-Riemanniennes admettant des géodésiques minimisantes singulières

2017

This thesis is devoted to the study of the Monge transport problem for the quadratic cost in sub-Riemannian geometry and the essential conditions to obtain existence and uniqueness of solutions. These works consist in extending these results to the case of sub-Riemannian structures admitting singular minimizing geodesics. In a first part, we develop techniques inspired by works by Cavalletti and Huesmann in order to obtain significant results for structures of rank 2 in dimension 4. In a second part, we study analytical tools of the h-semiconcavity of the sub-Riemannian distance and we show how this type of regularity can lead to the well-posedness of the Monge problem in general cases.

Monge problem[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Géométrie sous-RiemannienneGéodésiques minimisantes singulièresSingular minimizing geodesic[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Problème de MongeSub-Riemannian geometry
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