Local semiconvexity of Kantorovich potentials on non-compact manifolds*
ESAIM: Control, Optimisation and Calculus of Variations (2011)
- Volume: 17, Issue: 3, page 648-653
- ISSN: 1292-8119
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topFigalli, Alessio, and Gigli, Nicola. "Local semiconvexity of Kantorovich potentials on non-compact manifolds*." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 648-653. <http://eudml.org/doc/221919>.
@article{Figalli2011,
abstract = {
We prove that any Kantorovich potential for the cost function
c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex
in the “region of interest”, without any compactness assumption
on M, nor any assumption on its curvature. Such a region of
interest is of full μ-measure as soon as the starting measure
μ does not charge n – 1-dimensional rectifiable sets.
},
author = {Figalli, Alessio, Gigli, Nicola},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Kantorovich potential; optimal transport; regularity},
language = {eng},
month = {8},
number = {3},
pages = {648-653},
publisher = {EDP Sciences},
title = {Local semiconvexity of Kantorovich potentials on non-compact manifolds*},
url = {http://eudml.org/doc/221919},
volume = {17},
year = {2011},
}
TY - JOUR
AU - Figalli, Alessio
AU - Gigli, Nicola
TI - Local semiconvexity of Kantorovich potentials on non-compact manifolds*
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/8//
PB - EDP Sciences
VL - 17
IS - 3
SP - 648
EP - 653
AB -
We prove that any Kantorovich potential for the cost function
c = d2/2 on a Riemannian manifold (M, g) is locally semiconvex
in the “region of interest”, without any compactness assumption
on M, nor any assumption on its curvature. Such a region of
interest is of full μ-measure as soon as the starting measure
μ does not charge n – 1-dimensional rectifiable sets.
LA - eng
KW - Kantorovich potential; optimal transport; regularity
UR - http://eudml.org/doc/221919
ER -
References
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