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arXiv · 2402.04649

Some obstructions to contraction theorems on the half-sphere

Max Fathi·Matthieu Fradelizi·Nathael Gozlan·Simon Zugmeyer
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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.

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Max Fathi, Matthieu Fradelizi, Nathael Gozlan, Simon Zugmeyer. 2024-02-07. Some obstructions to contraction theorems on the half-sphere. https://arxiv.org/abs/2402.04649

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