Some obstructions to contraction theorems on the half-sphere
Functional Analysis
2024-02-08 v1 Probability
Abstract
Caffarelli's contraction theorem states that probability measures with uniformly logconcave densities on R d can be realized as the image of a standard Gaussian measure by a globally Lipschitz transport map. We discuss some counterexamples and obstructions that prevent a similar result from holding on the half-sphere endowed with a uniform measure, answering a question of Beck and Jerison.
Cite
@article{arxiv.2402.04649,
title = {Some obstructions to contraction theorems on the half-sphere},
author = {Max Fathi and Matthieu Fradelizi and Nathael Gozlan and Simon Zugmeyer},
journal= {arXiv preprint arXiv:2402.04649},
year = {2024}
}