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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.
Badreddine, Z. 1, 2
@article{AIHPC_2019__36_3_837_0,
author = {Badreddine, Z.},
title = {Mass transportation on {sub-Riemannian} structures of rank two in dimension four},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {837--860},
publisher = {Elsevier},
volume = {36},
number = {3},
year = {2019},
doi = {10.1016/j.anihpc.2018.10.003},
zbl = {1429.49046},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.10.003/}
}
TY - JOUR AU - Badreddine, Z. TI - Mass transportation on sub-Riemannian structures of rank two in dimension four JO - Annales de l'I.H.P. Analyse non linéaire PY - 2019 SP - 837 EP - 860 VL - 36 IS - 3 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.10.003/ DO - 10.1016/j.anihpc.2018.10.003 LA - en ID - AIHPC_2019__36_3_837_0 ER -
%0 Journal Article %A Badreddine, Z. %T Mass transportation on sub-Riemannian structures of rank two in dimension four %J Annales de l'I.H.P. Analyse non linéaire %D 2019 %P 837-860 %V 36 %N 3 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.10.003/ %R 10.1016/j.anihpc.2018.10.003 %G en %F AIHPC_2019__36_3_837_0
Badreddine, Z. Mass transportation on sub-Riemannian structures of rank two in dimension four. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 837-860. doi : 10.1016/j.anihpc.2018.10.003. http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.10.003/
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