Counterexamples to Continuity of Optimal Transport Maps on Positively Curved Riemannian Manifolds
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Publication:5302873
DOI10.1093/imrn/rnn120zbMath1160.49047arXiv0709.1653OpenAlexW2963384122WikidataQ115273738 ScholiaQ115273738MaRDI QIDQ5302873
Publication date: 15 January 2009
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0709.1653
Variational problems in a geometric measure-theoretic setting (49Q20) Global Riemannian geometry, including pinching (53C20) Manifolds of metrics (especially Riemannian) (58D17)
Related Items (12)
Regularity of optimal transport maps on multiple products of spheres ⋮ Optimal Transport and Curvature ⋮ The Monge–Ampère equation and its link to optimal transportation ⋮ On the Ma-Trudinger-Wang curvature on surfaces ⋮ Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces ⋮ Wasserstein barycenters over Riemannian manifolds ⋮ Regularity of optimal transport in curved geometry: the nonfocal case ⋮ The Ma-Trudinger-Wang curvature for natural mechanical actions ⋮ Continuity, curvature, and the general covariance of optimal transportation ⋮ Regularity of optimal transport maps on locally nearly spherical manifolds ⋮ Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2 ⋮ Partial regularity for optimal transport maps
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