Regularity for a log-concave to log-concave mass transfer problem with near Euclidean cost

Details Regularity for a log-concave to log-concave mass transfer problem with near Euclidean cost Regularity for a log-concave to log-concave mass transfer problem with near Euclidean cost

2010-07-22

arxiv.org/abs/1007.3890v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

If the cost function is not too far from the Euclidean cost, then the optimal
map transporting Gaussians restricted to a ball will be regular. \ Similarly,
given any cost function which is smooth in a neighborhood of two points on a
manifold, there are small neighborhoods near each such that a Gaussian
restricted to one is transported smoothly to a Gaussian on the other

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