Regularity of optimal transport on compact, locally nearly spherical, manifolds

DOI10.1515/CRELLE.2010.066zbMath1200.58025OpenAlexW2326035504MaRDI QIDQ3163863

Yuxin Ge, Philippe P. Delanoë

Publication date: 27 October 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2010.066

zbMATH Keywords

optimal transportelliptic equation of Monge-Ampère type

Mathematics Subject Classification ID

Transportation, logistics and supply chain management (90B06) Elliptic equations on manifolds, general theory (58J05) Applications of PDEs on manifolds (58J90) Monge-Ampère equations (35J96)

Related Items

Regularity of optimal transport maps on multiple products of spheres ⋮ The Monge–Ampère equation and its link to optimal transportation ⋮ A glimpse into the differential topology and geometry of optimal transport ⋮ On the Ma-Trudinger-Wang curvature on surfaces ⋮ Hölder continuity and injectivity of optimal maps ⋮ A Perturbative Approach to the Parabolic Optimal Transport Problem ⋮ Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces ⋮ Regularity in Monge's mass transfer problem ⋮ A perturbation argument for a Monge-Ampère type equation arising in optimal transportation ⋮ On the local geometry of maps with c-convex potentials ⋮ Regularity of optimal transport in curved geometry: the nonfocal case ⋮ Continuity and injectivity of optimal maps ⋮ 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 ⋮ Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds ⋮ Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations ⋮ Partial regularity for optimal transport maps

Cites Work

• Unnamed Item
• Lie solutions of Riemannian transport equations on compact manifolds
• Regularity of optimal transport in curved geometry: the nonfocal case
• A generalized sphere theorem
• The geometry of optimal transportation
• Gradient rearrangement for diffeomorphisms of a compact manifold.
• A geometric approximation to the Euler equations: the Vlasov-Monge-Ampère system
• Contributions to riemannian geometry in the large
• Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung
• Polar factorization and monotone rearrangement of vector‐valued functions
• Polar factorization of maps on Riemannian manifolds