Characterization of absolutely continuous curves in Wasserstein spaces
From MaRDI portal
Publication:859772
DOI10.1007/s00526-006-0032-2zbMath1132.60004OpenAlexW2101379442MaRDI QIDQ859772
Publication date: 18 January 2007
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-006-0032-2
Probability measures on topological spaces (60B05) Existence of optimal solutions to problems involving randomness (49J55)
Related Items (54)
A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients ⋮ Busemann functions on the Wasserstein space ⋮ On the geometry of geodesics in discrete optimal transport ⋮ Nonlinear mobility continuity equations and generalized displacement convexity ⋮ Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows ⋮ Li-Yau and Harnack type inequalities in \(\text{RCD}^\ast (K,N)\) metric measure spaces ⋮ Three superposition principles: currents, continuity equations and curves of measures ⋮ Weak and strong convergence of derivations and stability of flows with respect to MGH convergence ⋮ Optimal transport maps on Alexandrov spaces revisited ⋮ Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds ⋮ Lagrangian Discretization of Variational Mean Field Games ⋮ Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces ⋮ Convergence of a One-Dimensional Cahn--Hilliard Equation with Degenerate Mobility ⋮ On the differential structure of metric measure spaces and applications ⋮ From optimal transportation to optimal teleportation ⋮ Mean field approximation of an optimal control problem for the continuity equation arising in smart charging ⋮ On master test plans for the space of BV functions ⋮ Angles between curves in metric measure spaces ⋮ Hidden Dissipation and Convexity for Kimura Equations ⋮ Failure of strong unique continuation for harmonic functions on RCD spaces ⋮ Absolutely continuous and BV-curves in 1-Wasserstein spaces ⋮ An optimal transport formulation of the Einstein equations of general relativity ⋮ Equivalent definitions of very strict \textit{CD(K,N)}-spaces ⋮ Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures ⋮ Horo-functions associated to atom sequences on the Wasserstein space ⋮ Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below ⋮ From Monge to Higgs: a survey of distance computations in noncommutative geometry ⋮ Hamilton-Jacobi in metric spaces with a homological term ⋮ Absolutely continuous curves in extended Wasserstein−Orlicz spaces ⋮ Metric measure spaces with Riemannian Ricci curvature bounded from below ⋮ Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds ⋮ On one-dimensionality of metric measure spaces ⋮ Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates ⋮ Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures ⋮ Korevaar-Schoen's energy on strongly rectifiable spaces ⋮ Martingales associated to peacocks using the curtain coupling ⋮ On interpolation and curvature via Wasserstein geodesics ⋮ Equivalent definitions of \(BV\) space and of total variation on metric measure spaces ⋮ A survey on dynamical transport distances ⋮ One dimensional singular Cucker-Smale model: uniform-in-time mean-field limit and contractivity ⋮ Nonlinear diffusion equations with variable coefficients as gradient flows in Wasserstein spaces ⋮ An entropy generation formula on \(RCD(K,\infty)\) spaces ⋮ Characterizations of monotonicity of vector fields on metric measure spaces ⋮ Existence of optimal transport maps in very strict \(CD(K,\infty)\) -spaces ⋮ Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces ⋮ Gradient flow approach to local mean-field spin systems ⋮ Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves ⋮ The Markov-quantile process attached to a family of marginals ⋮ Structure of measures in Lipschitz differentiability spaces ⋮ Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure ⋮ Curves of minimal action over metric spaces ⋮ Sobolev-to-Lipschitz property on \({\mathsf{QCD}} \)-spaces and applications ⋮ The continuity equation on metric measure spaces ⋮ Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Transport equation and Cauchy problem for BV vector fields
- Path functionals over Wasserstein spaces
- Convex analysis and measurable multifunctions
- A convexity principle for interacting gases
- Monge-Kantorovitch measure transportation and Monge-Ampère equation on Wiener space
- Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
- Rectifiable sets in metric and Banach spaces
- A Riemannian interpolation inequality à la Borell, Brascamp and Lieb
- Measure transport on Wiener space and the Girsanov theorem.
- Convex functionals of probability measures and nonlinear diffusions on manifolds
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- Ricci curvature for metric-measure spaces via optimal transport
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Transport inequalities, gradient estimates, entropy and Ricci curvature
- The Variational Formulation of the Fokker--Planck Equation
- Eulerian Calculus for the Contraction in the Wasserstein Distance
This page was built for publication: Characterization of absolutely continuous curves in Wasserstein spaces