Counterexamples to continuity of optimal transportation on positively curved Riemannian manifolds

Abstract

Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.

arXiv comment10 pages

References in corpus (2)

• On the regularity of maps solutions of optimal transportation problems
• Continuity, curvature, and the general covariance of optimal transportation

Cited by in corpus (4)

• Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)
• Continuity, curvature, and the general covariance of optimal transportation
• A Jacobian inequality for gradient maps on the sphere and its application to directional statistics
• Parabolic optimal transport equations on manifolds