The Monge-Kantorovich problem: achievements, connections, and perspectives

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Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, result): “We also mention two very recent survey, [63] and [228]: the former accounts for the main achievements on the theory on the occasion of the centennial of the birth of L.”
Learning with a Wasserstein Loss (2015, background): “The penalty increases as more mass is transported over longer distances, according to the ground metric M .”
Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints (2015, methodology): “Second, we derive analogous continuity bounds for the von Neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint, most importantly systems of multiple quantum harmonic oscillators.”
Deep Learning for Free-Hand Sketch: A Survey (2020, methodology): “[304] proposed to represent 3D models by computing the Wasserstein distance [305] based barycenters of multiple projections of 3D”
Subgeometric rates of convergence of Markov processes in the Wasserstein metric (2012, unknown): “, [2]) that if d is a semimetric on E, then the Wasserstein semidistance Wd between probability measures μ,ν ∈ P(E) is given by Wd(μ, ν) := inf λ∈C(μ,ν) ∫ E×E d(x, y)λ(dx, dy),”