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.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité