Isoperimetric inequality and OMT

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A very interesting application of optimal transport is a proof of the isoperimetric inequality. The first proof with an OMT argument is due to Gromov and the main tool is the Knothe's map. [1].

  1. ↑ V.D. Milman, G. Schechtman, Asymptotic Theory of Finite-Dimensional Normed Spaces, with an appendix by M. Gromov, Lecture notes in Mathematics, vol. 1200 (Springer, Berlin, 1986)
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