Last week at MSRI we started a Brown Bag seminar informally named “Beautiful computations’ Seminar” (credit goes to Juan Luis Vazquez for the idea). The purpose of the seminar (which will be taking place on thursdays around lunch time) is having very short talks explaining a specific “trick” or idea that the speaker considers both beautiful and powerful.

For the first talk of this seminar I presented the proof of the Isoperimetric inequality using mass transport. The proof in this specific form was found independently by N. Trudinger and R. McCann, and it is certainly strongly influenced by work of M. Gromov which I am currently not competent to describe. Modulo the use of the Brenier-McCann theorem from Optimal transport, this is the shortest proof of the isoperimetric theorem (in general dimensions) that I am aware of .

Further, this method of proof has rather deep ramifications…

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