Jun Kitagawa

Regularity for the Optimal Transportation Problem with Euclidean Distance Squared Cost on the Embedded Sphere

We give sufficient conditions on initial and target measures supported on the sphere

On the Degeneracy of Optimal Transportation

\S^n

A parabolic flow toward solutions of the optimal transportation problem on domains with boundary

to ensure the solution to the optimal transport problem with the cost

On the local geometry of maps with c-convex potentials

|x-y|^2/2

A Newton algorithm for semi-discrete optimal transport

is a diffeomorphism.

An iterative scheme for solving the optimal transportation problem

We extend a dimensional upper bound on how much an optimal transport map can degenerate for the quadratic transportation cost, originally due to Caffarelli, to cost functions that satisfy the curvature condition of Ma, Trudinger, and Wang.

Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations

Abstract We consider a parabolic version of the mass transport problem, and show that a solution converges to a solution of the original mass transport problem under suitable conditions on the cost function, and initial and target domains.