Search results for "Monge problem"

showing 2 items of 2 documents

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
researchProduct

Convexities and optimal transport problems on the Wiener space

2013

The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dime…

Convexité[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Monge-Ampère equationConvexityMonge problem[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Dimension infinieTransport optimalLogarithmic concave measureWiener spaceEspace de WienerOptimal transportÉquation de Monge-AmpèreMesure logarithmiquement concaveProblème de MongeInfinite dimension
researchProduct