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Pré-Publication, Document De Travail Année : 2024

Some Obstructions To Contraction Theorems On The Half-sphere

Résumé

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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hal-04441540 , version 1 (06-02-2024)

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Max Fathi, Matthieu Fradelizi, Nathael Gozlan, Simon Zugmeyer. Some Obstructions To Contraction Theorems On The Half-sphere. 2024. ⟨hal-04441540⟩
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