12 may 2025

Aula T.1.1 (first floor) in the Edificio 13 of the Politecnico di Milano

Abstract.

The isoperimetric inequality has a long history in mathematics. In this lecture, we will discuss how the isoperimetric inequality can be generalized to submanifolds in Euclidean space. As a special case, we obtain a sharp isoperimetric inequality for minimal submanifolds of codimension at most 2, answering a question going back to work of Carleman. The proof of that inequality is inspired by, but does not actually use, optimal transport.

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