Communications in Analysis and Geometry

Volume 19 (2011)

Number 1

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

Pages: 191 – 208

DOI: http://dx.doi.org/10.4310/CAG.2011.v19.n1.a6

Author

Micah Warren (Department of Mathematics, Princeton University)

Abstract

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.

Full Text (PDF format)