Mass transportation and contractions

Abstract

According to a celebrated result of L. Caffarelli, every optimal mass transportation mapping pushing forward the standard Gaussian measure onto a log-concave measure $e^{-W}dx$ with $D^{2}W\ge Id$ is 1-Lipschitz. We present a short survey of related results and various applications.

13 pages, 27 references

References in corpus (1)

• A Generalization of Caffarelli's Contraction Theorem via (reverse) Heat Flow

Cited by in corpus (7)

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• Moment measures and stability for Gaussian inequalities
• Eigenvalue distribution of optimal transportation
• The Brownian transport map
• Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures
• Mirrored Langevin Dynamics
• On continuity equations in infinite dimensions with non-Gaussian reference measure