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Publication
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Extending a result of Caffarelli, we provide global Lipschitz changes of variables between compactly supported perturbations of log-concave measures. The result is based on a combination of ideas from optimal transportation theory and a new Pogorelov-type estimate. In the case of radially symmetric measures, Lipschitz changes of variables are obtained for a much broader class of perturbations.
Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan
Fabio Nobile, Sundar Subramaniam Ganesh