Optimal Transport

2008/10/25 by Cédric Villani · 13 citations
Mathematics · #Applied mathematics #Computer science #Convexity #Curvature #Displacement (psychology) #Duality (order theory) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Isoperimetric inequality #Mathematical analysis #Mathematics #Monotonic function #Nonlinear Partial Differential Equations #Pure mathematics #Ricci curvature #Smoothness

paper · doi:10.1007/978-3-540-71050-9

openalex publication_date 2008/10/25 · crossref created 2008/10/25 · crossref issued 2009/01/01 · crossref published 2009/01/01 · crossref published-print 2009/01/01 · crossref deposited 2019/04/06 · openalex created_date 2022/05/12 · openalex updated_date 2026/08/04 · crossref indexed 2026/08/06

Citations

• A Review of Mathematical Topics in Collisional Kinetic Theory
• Dynamical Theories of Brownian Motion
• Some Remarks on Transportation Cost and Related Inequalities
• A criterion for Talagrand's quadratic transportation cost inequality
• Ricci curvature for metric-measure spaces via optimal transport
• On the parabolic kernel of the Schrödinger operator
• Concentration of measure and isoperimetric inequalities in product spaces
• Remarks on a Multivariate Transformation
• A Mathematical Theory of Communication
• Mathematics of Granular Materials
• The Brunn-Minkowski inequality
• Theory of Statistical Estimation
• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products
• Quasiconformal maps in metric spaces with controlled geometry
• Action minimizing invariant measures for positive definite Lagrangian systems
• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential
• The geometry of optimal transportation
• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality
• Derivation of the Schrödinger Equation from Newtonian Mechanics
• Continuity of Solutions of Parabolic and Elliptic Equations
• Logarithmic Sobolev Inequalities
• Some geometric calculations on Wasserstein space
• On the regularity of maps solutions of optimal transportation problems

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• Cutting down trees with a Markov chainsaw
• Explainable Regime Aware Investing
• A Liouville theorem for bounded empirical-harmonic functions on P₂(M)
• New approaches to almost i.i.d. information theory
• cuRegOT: A GPU-Accelerated Solver for Entropic-Regularized Optimal Transport
• A Measure-Theoretic Transport Formulation of Galaxy Evolution on the Galaxy Manifold: Geometric Constraints
• Multi-Period Martingale Optimal Transport: Classical Theory, Neural Acceleration, and Financial Applications
• Surrogate Trajectories Along Probability Flows: Pseudo Markovian Alternative to Mori Zwanzig
• Ergodic control of McKean-Vlasov systems on the Wasserstein space
• Colloquium: Quantum root-mean-square error and measurement uncertainty relations
• Gromov's compactness theorem (geometry) [wikipedia]
• Monge–Ampère equation [wikipedia]