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# 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

#### 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.