The Monge problem for distance cost in geodesic spaces

DOI10.1007/s00220-013-1663-8zbMath1275.49080arXiv1103.2796OpenAlexW1996897596MaRDI QIDQ1944833

Fabio Cavalletti, Stefano Bianchini

Publication date: 28 March 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.2796

zbMATH Keywords

Monge transport problemnon-branching geodesic spaces

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geodesics in global differential geometry (53C22)

Related Items (33)

Characterization of low dimensional \(RCD^\ast(K, N)\) spaces ⋮ The Monge Problem in Geodesic Spaces ⋮ Non-compact \(\mathrm{RCD}(0,N)\) spaces with linear volume growth ⋮ Needle decompositions and isoperimetric inequalities in Finsler geometry ⋮ Optimal transport maps on Alexandrov spaces revisited ⋮ New formulas for the Laplacian of distance functions and applications ⋮ Weighted Beckmann problem with boundary costs ⋮ Isoperimetric inequality in noncompact 𝖬𝖢𝖯 spaces ⋮ Minimizing optimal transport for functions with fixed-size nodal sets ⋮ Existence and uniqueness of optimal transport maps ⋮ A review of Lorentzian synthetic theory of timelike Ricci curvature bounds ⋮ Geometry of vectorial martingale optimal transportations and duality ⋮ An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth ⋮ The globalization theorem for \(\mathrm{CD}(K, N)\) on locally finite spaces ⋮ Optimal maps in essentially non-branching spaces ⋮ Local isoperimetric inequalities in metric measure spaces verifying measure contraction property ⋮ Monge problem in metric measure spaces with Riemannian curvature-dimension condition ⋮ Decomposition of geodesics in the Wasserstein space and the globalization problem ⋮ Structure of optimal martingale transport plans in general dimensions ⋮ The globalization theorem for the curvature-dimension condition ⋮ On weak super Ricci flow through neckpinch ⋮ Optimal martingale transport between radially symmetric marginals in general dimensions ⋮ Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds ⋮ Sharp Poincaré inequalities under Measure Contraction Property ⋮ On the topology and the boundary of \(N\)-dimensional \(\mathsf{RCD}\,(K,N)\) spaces ⋮ Displacement convexity of entropy and the distance cost optimal transportation ⋮ Indeterminacy estimates and the size of nodal sets in singular spaces ⋮ On the existence of dual solutions for Lorentzian cost functions ⋮ On the equality of values in the Monge and Kantorovich problems ⋮ Isoperimetric inequality under measure-contraction property ⋮ Optimal transportation, topology and uniqueness ⋮ Optimal transportation in \(\mathbb R^n\) for a distance cost with a convex constraint ⋮ Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Monge problem in \(\mathbb R^d\)
• On the Euler-Lagrange equation for a variational problem: The general case. II
• Stability of a 4th-order curvature condition arising in optimal transport theory
• Existence of optimal transport maps for crystalline norms
• Ricci curvature for metric-measure spaces via optimal transport
• On the measure contraction property of metric measure spaces
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Constructing optimal maps for Monge’s transport problem as a limit of strictly convex costs
• Monge’s transport problem on a Riemannian manifold
• Differential equations methods for the Monge-Kantorovich mass transfer problem
• A compact set of disjoint line segments in E ³ whose end set has positive measure
• Currents in metric spaces
• On the Monge mass transfer problem

This page was built for publication: The Monge problem for distance cost in geodesic spaces