Stability of a 4th-order curvature condition arising in optimal transport theory

DOI10.1016/j.jfa.2008.07.003zbMath1158.53036OpenAlexW2117851225WikidataQ125886546 ScholiaQ125886546MaRDI QIDQ999864

Publication date: 10 February 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.07.003

zbMATH Keywords

optimal transport Gromov-Hausdorff convergence Ma-Trudinger-Wang condition

Mathematics Subject Classification ID

Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Optimality conditions (49K99)

Related Items

Gradient flow and entropy inequalities for quantum Markov semigroups with detailed balance, Emergence via non-existence of averages, On robust portfolio and naïve diversification: mixing ambiguous and unambiguous assets, A weak semantic approach to bisimulation metrics in models with nondeterminism and continuous state spaces, Point source regularization of the finite source reflector problem, A fitness-driven cross-diffusion system from population dynamics as a gradient flow, On the \(c\)-concavity with respect to the quadratic cost on a manifold, Nonlinear mobility continuity equations and generalized displacement convexity, Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients, On singular sets of \(c\)-concave functions, When optimal transport meets information geometry, Synthetic theory of Ricci curvature bounds, Limit laws for empirical optimal solutions in random linear programs, A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures, Wasserstein stability of porous medium-type equations on manifolds with Ricci curvature bounded below, Polish spaces of causal curves, Sign intermixing for Riesz bases and frames measured in the Kantorovich-Rubinstein norm, Partition-based distributionally robust optimization via optimal transport with order cone constraints, The diffusion geometry of fibre bundles: horizontal diffusion maps, On the Ma-Trudinger-Wang curvature on surfaces, Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics, Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension, Product assortment and space allocation strategies to attract loyal and non-loyal customers, Compositionally-warped Gaussian processes, Contractive barycentric maps and \(L^{1}\) ergodic theorems on the cone of positive definite matrices, Transportation distances on the circle, Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces, Concavification of free entropy, Graphon particle system: uniform-in-time concentration bounds, Existence and uniqueness of optimal transport maps, The Dyson and Coulomb games, Probabilistic analysis of a general class of nonlinear random differential equations with state-dependent impulsive terms via probability density functions, Infinite-dimensional porous media equations and optimal transportation, Central limit theorem for Markov processes with spectral gap in the Wasserstein metric, The Monge problem for distance cost in geodesic spaces, The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities, Multiplicative Schrödinger problem and the Dirichlet transport, Local curvature-dimension condition implies measure-contraction property, Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox, Horo-functions associated to atom sequences on the Wasserstein space, Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting, Parameterized Wasserstein means, Gradient flows for non-smooth interaction potentials, Denoising of diffusion magnetic resonance images using a modified and differentiable Monge-Kantorovich distance for measure-valued functions, The Monge problem in Wiener space, Heat kernel on Ricci shrinkers, Second derivative estimates for uniformly elliptic operators on Riemannian manifolds, Sequential Monte Carlo with kernel embedded mappings: the mapping particle filter, Positivity of Ma-Trudinger-Wang curvature on Riemannian surfaces, Regular sensitivity computation avoiding chaotic effects in particle-in-cell plasma methods, Wasserstein distance to independence models, Bipolar comparison, Mass transportation on sub-Riemannian structures of rank two in dimension four, On the local geometry of maps with c-convex potentials, Sample-based population observers, Generalized solutions for inextensible string equations, Optimal allocation of an indivisible good, A new multicomponent Poincaré-Beckner inequality, Regularity of optimal transport in curved geometry: the nonfocal case, Fast iterative solvers for an optimal transport problem, Gradient flow of the Chapman-Rubinstein-Schatzman model for signed vortices, The behavior of solutions of multidimensional aggregation equations with mildly singular interaction kernels, A Monge-Kantorovich mass transport problem for a discrete distance, A description of transport cost for signed measures, On asymptotic behaviour and \(W^{2, p}\) regularity of potentials in optimal transportation, Optimal transport natural gradient for statistical manifolds with continuous sample space, Strassen's theorem for quantum couplings, Nonlinear Fokker-Planck equations with reaction as gradient flows of the free energy, Duality on gradient estimates and Wasserstein controls, Bishop-Gromov type inequality on Ricci limit spaces, One dimensional singular Cucker-Smale model: uniform-in-time mean-field limit and contractivity, Higher order regularity of nonlinear Fokker-Planck PDEs with respect to the measure component, Martingale optimal transport in the discrete case via simple linear programming techniques, A splitting method for nonlinear diffusions with nonlocal, nonpotential drifts, Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds, Convex Sobolev inequalities related to unbalanced optimal transport, Ricci curvature of Markov chains on metric spaces, Uniform convexity and smoothness, and their applications in Finsler geometry, Conditional nonlinear expectations, An explicit martingale version of the one-dimensional Brenier's theorem with full marginals constraint, A new class of transport distances between measures, Small noise limit and convexity for generalized incompressible flows, Schrödinger problems, and optimal transport, Some results on Sobolev spaces with respect to a measure and applications to a new transport problem, Empirical geodesic graphs and CAT\((k)\) metrics for data analysis, Multi-species optimal transportation, The Hermite-Hadamard inequality in higher dimensions, Mass transportation and rough curvature bounds for discrete spaces, The quadratic Wasserstein metric for earthquake location, Necessary and sufficient conditions for continuity of optimal transport maps on Riemannian manifolds, The \(\alpha \)-dependence of the invariant measure of stochastic real Ginzburg-Landau equation driven by \(\alpha \)-stable Lévy processes, On the Bures-Wasserstein distance between positive definite matrices, On the choice of weight functions for linear representations of persistence diagrams, Relating relative entropy, optimal transport and Fisher information: a quantum HWI inequality, Strong law of large numbers for the \(L^1\)-Karcher mean, On open flat sets in spaces with bipolar comparison, Model of phenotypic evolution in hermaphroditic populations, Cortically based optimal transport, Robustness to incorrect models and data-driven learning in average-cost optimal stochastic control, Recent developments on the MTW tensor, Graph-Based Equilibrium Metrics for Dynamic Supply–Demand Systems With Applications to Ride-sourcing Platforms, A superposition principle for the inhomogeneous continuity equation with Hellinger–Kantorovich-regular coefficients, Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes, Linear-sized independent sets in random cographs and increasing subsequences in separable permutations, Approximate message passing with spectral initialization for generalized linear models*, Entropic Measure on Multidimensional Spaces, Optimal Transport and Curvature, Portfolio optimization with a prescribed terminal wealth distribution, On the Degeneracy of Optimal Transportation, The negative of regular cosmological time function is a viscosity solution, Distribution regression model with a Reproducing Kernel Hilbert Space approach, An analytical framework for consensus-based global optimization method, Optimal Estimation of Wasserstein Distance on a Tree With an Application to Microbiome Studies, Generative abstraction of Markov population processes, Advanced Multilevel Monte Carlo Methods, Optimal transport and variational Bayesian inference, The transport problem for non-additive measures, Importance sampling for McKean-Vlasov SDEs, Adaptive mesh methods on compact manifolds via optimal transport and optimal information transport, The Wasserstein geometry of nonlinear σ models and the Hamilton–Perelman Ricci flow, Conformal mirror descent with logarithmic divergences, Bounds on Choquet risk measures in finite product spaces with ambiguous marginals, Conic linear optimization for computer-assisted proofs. Abstracts from the workshop held April 10--16, 2022, METRIC THICKENINGS, BORSUK–ULAM THEOREMS, AND ORBITOPES, Geometry of sample spaces, An optimal transport-based characterization of convex order, Wasserstein adversarial learning based temporal knowledge graph embedding, Approximations for Probability Distributions and Stochastic Optimization Problems, Concentration of quantum states from quantum functional and transportation cost inequalities, Combined mean field limit and non-relativistic limit of Vlasov–Maxwell particle system to Vlasov–Poisson system, Highly irregular orbits for subshifts of finite type: large intersections and emergence, The Friedland–Hayman inequality and Caffarelli’s contraction theorem, Strong convexity of sandwiched entropies and related optimization problems, On the heat flow on metric measure spaces: existence, uniqueness and stability, ITERATED FUNCTION SYSTEMS WITH PLACE-DEPENDENT PROBABILITIES AND THE INVERSE PROBLEM OF MEASURE APPROXIMATION USING MOMENTS, Some new results on relative entropy production, time reversal, and optimal control of time-inhomogeneous diffusion processes, Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊², Optimal transport in full-waveform inversion: analysis and practice of the multidimensional Kantorovich–Rubinstein norm, Analysis of seismic inversion with optimal transportation and softplus encoding, Density-aware decentralised multi-agent exploration with energy constraint based on optimal transport theory, Towards the smoothness of optimal maps on Riemannian submersions and Riemannian products (of round spheres in particular)

Cites Work