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15 February 2010 Regularity of optimal transport in curved geometry: The nonfocal case
Grégoire Loeper, Cédric Villani
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Duke Math. J. 151(3): 431-485 (15 February 2010). DOI: 10.1215/00127094-2010-003

Abstract

We explore some geometric and analytic consequences of a curvature condition introduced by Ma, Trudinger, and Wang in relation to the smoothness of optimal transport in curved geometry. We discuss a conjecture according to which a strict version of the Ma-Trudinger-Wang condition is sufficient to prove regularity of optimal transport on a Riemannian manifold. We prove this conjecture under a somewhat restrictive additional assumption of nonfocality; at the same time, we establish the striking geometric property that the tangent cut locus is the boundary of a convex set. Partial extensions are presented to the case when there is no pure focalization on the tangent cut locus

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Grégoire Loeper. Cédric Villani. "Regularity of optimal transport in curved geometry: The nonfocal case." Duke Math. J. 151 (3) 431 - 485, 15 February 2010. https://doi.org/10.1215/00127094-2010-003

Information

Published: 15 February 2010
First available in Project Euclid: 8 February 2010

zbMATH: 1192.53041
MathSciNet: MR2605867
Digital Object Identifier: 10.1215/00127094-2010-003

Subjects:
Primary: 35J60
Secondary: 49Q20, 53C20

Rights: Copyright © 2010 Duke University Press

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Vol.151 • No. 3 • 15 February 2010
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