Transport problems and disintegration maps

and Soviet :union:'s Soft Disintegration

One of the main factors leading to the collapse of USSR is soft and non-military aspect. Unlike western and US attitude toward USSR's disintegration that attributes this event to themselves and their measures especially soft and media war, Islamic revolution of Iran has been ignored while it is the most basic phenomenon that has deeply influenced disintegration of USSR. Two key factors should ...

Existence and Uniqueness of Optimal Transport Maps

Let (X, d,m) be a proper, non-branching, metric measure space. We show existence and uniqueness of optimal transport maps for cost written as non-decreasing and strictly convex functions of the distance, provided (X, d,m) satisfies a new weak property concerning the behavior of m under the shrinking of sets to points, see Assumption 1. This in particular covers spaces satisfying the measure con...

Regularity of optimal transport maps and applications

Regularity of Optimal Transport Maps

In the special case “cost=squared distance” on R, the problem was solved by Caffarelli [Caf1, Caf2, Caf3, Caf4], who proved the smoothness of the map under suitable assumptions on the regularity of the densities and on the geometry of their support. However, a major open problem in the theory was the question of regularity for more general cost functions, or for the case “cost=squared distance”...

Transport in Two-Dimensional Maps

We study transport in the two-dimensional phase space of C r diffeomorphisms (r ~ 1) of two manifolds between regions of the phase space bounded by pieces of the stable and unstable manifolds of hyperbolic fixed points. The mechanism for the transport is associated with the dynamics of homoclinic and heteroclinic tangles, and the study of this dynamics leads to a general formulation for the tra...