At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

We give a necessary and sufficient condition on the cost function so that the map solution of
Monge's optimal transportation problem is continuous for arbitrary smooth positive data. This …

Let M and M be n-dimensional manifolds equipped with suitable Borel probability measures
ρ and ρ. For subdomains M and M of Rn, Ma, Trudinger & Wang gave sufficient conditions …

We show that the discrete Sinkhorn algorithm—as applied in the setting of Optimal Transport
on a compact manifold—converges to the solution of a fully non-linear parabolic PDE of …

The article describes the reflector problem in anisotropic media to study reflecting surfaces
to reshape electromagnetic radiation in a prescribed manner. It reviews the Snell law of …

Building on the results of M a et al.(in Arch. Rational Mech. Anal. 177 (2), 151–183 (2005)),
and of the author L oeper (in Acta Math., to appear), we study two problems of optimal …

Consider transportation of one distribution of mass onto another, chosen to optimize the total
expected cost, where cost per unit mass transported from x to y is given by a smooth function …

We present an abstract method in the setting of compact metric spaces which is applied to
solve a number of problems in geometric optics. In particular, we solve the one source near …

Monge-Ampère problems with non-quadratic cost function : application to freeform optics Page
1 Monge-Ampère problems with non-quadratic cost function : application to freeform optics …

This note concerns the relationship between conditions on cost functions and domains, the
convexity properties of potentials in optimal transportation and the continuity of the …