Isoperimetric inequality and OMT: Difference between revisions
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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. <ref>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)</ref>. | 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. <ref>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)</ref>. This proof is based on an idea by Knothe <ref> Herbert Knothe. "Contributions to the theory of convex bodies.." Michigan Math. J. 4 (1) 39 - 52, 1957 <ref> | ||
Revision as of 23:01, 11 February 2022
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]. This proof is based on an idea by Knothe <ref> Herbert Knothe. "Contributions to the theory of convex bodies.." Michigan Math. J. 4 (1) 39 - 52, 1957 <ref>
- ↑ 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)